All practice questions

Question 381Question →

An aviation structural mechanic is cutting a piece of sheet metal to repair an aircraft fuselage. The initial piece of sheet metal is $45 \frac{1}{2}$ inches long. The mechanic cuts off one piece that is $14 \frac{3}{4}$ inches long and another piece that is $18 \frac{5}{8}$ inches long. Assuming no material is lost to the saw cut, how many inches of the sheet metal remain? (Enter your answer as a decimal).

Show answer & explanation

Answer: 12.125

Answer

The remaining piece of sheet metal is 12.125 inches long.

The remaining length is correctly found by determining the sum of the removed parts (

14 \frac{3}{4} + 18 \frac{5}{8} = 33 \frac{3}{8}

) and subtracting it from the whole (

45 \frac{1}{2} - 33 \frac{3}{8} = 12 \frac{1}{8}

), which equals 12.125 inches.

Step-by-Step Solution

1

Find a common denominator for the fractional parts to easily add and subtract the lengths.

The least common denominator for 2, 4, and 8 is 8. The initial length is

45 \frac{4}{8}

inches. The first cut is

14 \frac{6}{8}

inches, and the second cut is

18 \frac{5}{8}

inches.

Fractions must have the same denominator before they can be added or subtracted.

2

Calculate the total length of the sheet metal that was cut off.

14 \frac{6}{8} + 18 \frac{5}{8} = 32 \frac{11}{8}

, which simplifies to

33 \frac{3}{8}

inches.

Adding the cut pieces together gives the total amount of material removed.

3

Subtract the total cut length from the initial length to find the remaining amount.

45 \frac{4}{8} - 33 \frac{3}{8} = 12 \frac{1}{8}

inches.

Subtracting the removed material from the starting material leaves the remaining balance.

4

Convert the final mixed number to a decimal.

12 \frac{1}{8} = 12.125

The question requires a decimal format for the numeric entry.

Key Concept

Adding and subtracting mixed numbers with unlike denominators in a practical context.

Question 382Question →

An ion with a $+3$ positive charge has $10$ electrons and a mass number of $27$ . How many neutrons are located inside the nucleus of this ion?

Show answer & explanation

Answer: 14

Answer

14 neutrons

For any atom or ion, the mass number equals the total count of protons and neutrons in the nucleus. Because this ion has a

+3

charge and

10

electrons, it must contain

13

protons (

10 + 3

). Subtracting

13

protons from the mass number of

27

gives exactly

14

neutrons.

Step-by-Step Solution

1

Calculate the atomic number (number of protons) using the ion's charge and electron count.

The atom has

13

protons.

A positive charge (

+3

) indicates that the atom has lost

3

electrons relative to its proton count. Therefore,

\text{Protons} = \text{Electrons} + \text{Charge} = 10 + 3 = 13

.

2

Calculate the number of neutrons using the mass number and the proton count.

The nucleus contains

14

neutrons.

Mass number is the sum of protons and neutrons (

A = Z + N

). Thus,

\text{Neutrons} = \text{Mass Number} - \text{Protons} = 27 - 13 = 14

.

Key Concept

Relationship between mass number, atomic number (protons), net ionic charge, and subatomic particle counts.

Estimated Time:1m 0s

Question 383Question →

A combat engineering squad fills $150$ sandbags in $40$ minutes. Operating at this exact constant rate, how many sandbags can the squad fill in $4$ hours?

Show answer & explanation

Answer: 900

Answer

900

Because the production rate is constant, the number of sandbags filled is directly proportional to the time spent. Harmonizing the time units by converting

4

hours into

240

minutes allows you to correctly scale up the initial ratio of

150

sandbags per

40

minutes.

Step-by-Step Solution

1

Convert the total working time from hours to minutes.

4 \text{ hours} \times 60 \text{ minutes/hour} = 240 \text{ minutes}

The given rate is in minutes (

150

sandbags per

40

minutes), so the target time must also be in minutes to set up an accurate proportion.

2

Set up a direct proportion.

\frac{150 \text{ sandbags}}{40 \text{ minutes}} = \frac{x \text{ sandbags}}{240 \text{ minutes}}

Since the squad works at a constant rate, the ratio of sandbags filled to time spent must remain equal.

3

Solve the proportion for

x

.

x = 900

The denominator

40

must be multiplied by

6

to get

240

. To keep the fraction equivalent, multiply the numerator

150

by

6

, yielding

900

.

Key Concept

Direct Proportions with Unit Harmonization

Estimated Time:1m 0s

Question 384Question →

A customer orders groceries through a delivery service. The subtotal of the groceries is $\$50.00$ . The service charges a $10\%$ delivery fee and an $8\%$ sales tax, both calculated on the grocery subtotal. The customer then adds a $20\%$ tip, which is calculated on the amount after the delivery fee and tax are applied. What is the total final cost to the customer?

Show answer & explanation

Answer: 70.8

Answer

70.80

The final cost is found by first determining the intermediate amount after the fee and tax are added to the subtotal. The delivery fee is

\$5.00

(

10\%

of

\$50

) and the tax is

\$4.00

(

8\%

of

\$50

), bringing the intermediate total to

\$59.00

. The

20\%

tip is calculated sequentially on this

\$59.00

amount, which equals

\$11.80

. Adding the tip to the intermediate total yields the final cost of

\$70.80

.

Step-by-Step Solution

1

Calculate the delivery fee based on the subtotal.

\$50.00 \times 0.10 = \$5.00

The problem states the

10\%

delivery fee is calculated on the grocery subtotal.

2

Calculate the sales tax based on the subtotal.

\$50.00 \times 0.08 = \$4.00

The problem states the

8\%

sales tax is also calculated on the grocery subtotal.

3

Calculate the intermediate total before the tip.

\$50.00 + \$5.00 + \$4.00 = \$59.00

The tip is based on the amount after the delivery fee and tax are applied, so we must find this intermediate total.

4

Calculate the tip based on the intermediate total.

\$59.00 \times 0.20 = \$11.80

The

20\%

tip is applied to the intermediate total of

\$59.00

.

5

Calculate the final cost to the customer.

\$59.00 + \$11.80 = \$70.80

The final cost is the sum of the intermediate total and the tip.

Key Concept

Calculating sequential percentages for taxes, fees, and tips on a base amount.

Question 385Question →

A homeowner hires a landscaping service for an original quoted price of $\$450.00$ . The company applies a $15\%$ promotional discount to this price. A local service tax of $8\%$ is then calculated based on the discounted amount. Finally, the homeowner adds a tip for the workers equal to $20\%$ of the original quoted price. What is the total amount, in dollars, that the homeowner pays?

Show answer & explanation

Answer: 503.1

Answer

503.10

The final amount is the sum of the discounted price, the tax calculated on the discounted price, and the tip calculated on the original price. Adding

\$382.50

,

\$30.60

, and

\$90.00

yields a final total of

\$503.10

.

Step-by-Step Solution

1

Calculate the discount amount.

\$67.50

The discount is

15\%

of the original

\$450.00

price.

2

Determine the discounted subtotal.

\$382.50

Subtract the

\$67.50

discount from the original

\$450.00

price.

3

Calculate the service tax.

\$30.60

The

8\%

tax is applied to the discounted subtotal of

\$382.50

.

4

Calculate the tip amount.

\$90.00

The

20\%

tip is based on the original quoted price of

\$450.00

.

5

Calculate the final total cost.

\$503.10

Add the discounted subtotal (

\$382.50

), tax (

\$30.60

), and tip (

\$90.00

).

Key Concept

Calculating sequential percentage changes, including taxes on discounted amounts and tips on original amounts.

Question 386Question →

A maintenance crew uses $4$ identical pumps to empty a large aviation fuel tank in $12$ hours. If the crew decides to use $6$ of these identical pumps instead, how many hours will it take to completely empty the tank?

Show answer & explanation

Answer: 8

Answer

8 hours

Because the number of pumps and time are inversely proportional, their product must remain constant. The initial scenario gives a product of 4 pumps × 12 hours = 48 pump-hours. To find the new time, divide the constant product of 48 by the new number of pumps (6). 48 ÷ 6 = 8 hours.

Step-by-Step Solution

1

Identify the mathematical relationship between the variables.

The number of pumps and the time required are inversely proportional.

When working at a constant rate, increasing the number of machines decreases the time needed to complete the same job.

2

Set up the inverse proportion equation.

4 \times 12 = 6 \times x

For inverse proportions, the product of the two variables remains constant (

x_1 y_1 = x_2 y_2

).

3

Calculate the total pump-hours and solve for the new time.

x = 48 \div 6 = 8

Dividing the constant product (48) by the new number of pumps (6) isolates the unknown time variable.

Key Concept

Inverse Proportions

Estimated Time:45s

Question 387Question →

An isotope of an alkaline earth metal located in Period 4 (Group 2) of the periodic table contains $24$ neutrons in its nucleus. What is the mass number of this neutral isotope?

Show answer & explanation

Answer: 44

Answer

44

An element in Group 2 and Period 4 of the periodic table is calcium (

\text{Ca}

), which has an atomic number of

20

. This means every calcium atom contains

20

protons in its nucleus. The mass number of an isotope is the total number of protons and neutrons combined:

20\text{ protons} + 24\text{ neutrons} = 44

.

Step-by-Step Solution

1

Determine the atomic number of the element using its periodic table position.

Atomic number is

20

(contains

20

protons).

The alkaline earth metal (Group 2) in Period 4 is calcium (

\text{Ca}

), which has an atomic number of

20

.

2

Calculate the mass number by summing the number of protons and neutrons.

\text{Mass number} = 20 + 24 = 44

.

The mass number (

A

) is defined as the total count of nucleons (protons plus neutrons) in the nucleus.

Key Concept

Determining mass number from periodic table position and subatomic particle counts

Estimated Time:1m 0s

Question 388Question →

A military supply convoy consumes $24$ gallons of diesel fuel to travel $140$ miles. Assuming the fuel consumption rate remains constant, how many gallons of diesel fuel are required for the convoy to travel a distance of $315$ miles?

Show answer & explanation

Answer: 54

Answer

54

By setting up a direct proportion between the distance traveled and the fuel consumed (

\frac{140}{24} = \frac{315}{x}

) and cross-multiplying, we solve for

x

and determine that the convoy requires exactly

54

gallons of fuel.

Step-by-Step Solution

1

Set up a direct proportion relating distance to fuel consumption.

\frac{140}{24} = \frac{315}{x}

Since the fuel consumption rate is constant, the ratio of miles traveled to gallons consumed remains the same.

2

Cross-multiply the proportion.

140x = 24 \times 315

Cross-multiplication converts the proportion into a linear equation to solve for the unknown variable

x

.

3

Simplify the right side of the equation.

140x = 7560

Multiplying the known values prepares the equation for the final isolation step.

4

Divide by

140

to solve for

x

.

x = \frac{7560}{140} = 54

Dividing both sides by

140

isolates

x

, revealing the required gallons of fuel.

Key Concept

Direct Proportions

Estimated Time:1m 0s

Question 389Question →

A recruit gets a haircut at the base exchange that costs $\$11.35$ . If he pays with a $\$20.00$ bill, how much change should he receive in dollars?

Show answer & explanation

Answer: 8.65

Answer

8.65

The correct change is found by setting up a subtraction equation where the cost (

\$11.35

) is subtracted from the payment amount (

\$20.00

). Proper alignment of the decimals and borrowing across the zeros gives exactly

8.65

.

Step-by-Step Solution

1

Align the decimals to subtract the cost of the haircut from the amount paid.

20.00 - 11.35

To find the change due, you must subtract the total purchase cost from the cash provided.

2

Perform the subtraction, properly borrowing across the zeros in 20.00.

8.65

Subtracting 11.35 from 20.00 yields the exact amount of change owed.

Key Concept

Calculating change by subtracting decimals.

Question 390Question →

A city planner is designing a rectangular public square that measures $60 \text{ yards}$ by $40 \text{ yards}$ . The entire square will be paved with brick, except for a central rectangular fountain that measures $10 \text{ yards}$ by $8 \text{ yards}$ . If the paving bricks cost $\$2.50$ per square foot, what is the total cost of the bricks needed for the square in dollars?

Show answer & explanation

Answer: 52200

Answer

52200

The correct answer is

52200 because the net area of the square to be paved is

2,320

square yards (

2400 \text{ sq yd total} - 80 \text{ sq yd fountain}

). Since

1

square yard equals

9

square feet, this converts to

20,880

square feet. Multiplying the total square footage by the brick cost of

\

2.50

per square foot yields a total cost of

\$52,200

.

Step-by-Step Solution

1

Calculate the total area of the public square in square yards.

2400 \text{ sq yd}

The total area is the product of its length and width (

60 \text{ yards} \times 40 \text{ yards}

).

2

Calculate the area of the central fountain in square yards.

80 \text{ sq yd}

The area of the fountain is the product of its length and width (

10 \text{ yards} \times 8 \text{ yards}

).

3

Subtract the fountain's area from the total area to find the net paved area in square yards.

2320 \text{ sq yd}

The fountain will not be paved, so its area must be removed from the total square yardage (

2400 - 80

).

4

Convert the net area from square yards to square feet.

20880 \text{ sq ft}

The cost of the bricks is given per square foot. Since

1 \text{ yard} = 3 \text{ feet}

,

1 \text{ square yard} = 3 \times 3 = 9 \text{ square feet}

. Therefore, we multiply the area in square yards by

9

(

2320 \times 9 = 20880

).

5

Calculate the total cost by multiplying the net area in square feet by the price per square foot.

52200

Multiplying the total square footage (

20880

) by the cost per square foot (

\$2.50

) yields the final cost in dollars.

Key Concept

Subtractive area calculations and square unit conversions

Question 391Question →

A ferry transports vehicles from the mainland to an island $18$ miles away. The ferry travels to the island at a speed of $9$ miles per hour and returns to the mainland along the same route at a speed of $6$ miles per hour.

How many hours does the complete round trip take?

Show answer & explanation

Answer: 5

Answer

The complete round trip takes 5 hours.

The round trip consists of two legs with different speeds. The outbound leg takes

18 \div 9 = 2

hours. The return leg takes

18 \div 6 = 3

hours. Adding these together yields a total time of

5

hours for the entire trip.

Step-by-Step Solution

1

Calculate the time taken for the outbound trip.

18 \div 9 = 2

hours

Time is equal to distance divided by rate. This gives the time spent traveling to the island.

2

Calculate the time taken for the return trip.

18 \div 6 = 3

hours

The return trip covers the same distance but at a slower speed.

3

Calculate the total round-trip time.

2 + 3 = 5

hours

The total time for a round trip is the sum of the time spent on each individual leg.

Key Concept

Calculating total round-trip time by finding the time for each leg separately.

Question 392Question →

A contractor is preparing to apply sealant to a new rectangular patio that measures $14$ yards in length and $5$ yards in width. If the sealant costs $3$ dollars per square yard, what is the total cost, in dollars, to seal the entire patio?

Show answer & explanation

Answer: 210

Answer

210

To find the total cost, you must first determine the area of the patio by multiplying the length (

14

yards) by the width (

5

yards), which equals

70

square yards. Then, multiply this area by the cost per square yard (

3

dollars) to get the total cost of

210

dollars.

Step-by-Step Solution

1

Calculate the area of the rectangular patio.

Area =

14 \times 5 = 70

square yards

The cost of the sealant is based on the surface area of the patio.

2

Calculate the total cost to seal the patio.

Total cost =

70 \times 3 = 210

dollars

Multiplying the total square yards by the price per square yard gives the final cost.

Key Concept

Calculating rectangular area and applying a unit rate.

Question 393Question →

A cyclist travels from her home to a nearby town, a distance of $15$ miles, at an average speed of $12$ mph. On the return trip along the same route, her average speed is $20$ mph. What is her average speed, in mph, for the entire round trip?

Show answer & explanation

Answer: 15

Answer

15

The correct average speed is found by dividing the total round-trip distance (

30

miles) by the total travel time (

2

hours), resulting in

15

mph.

Step-by-Step Solution

1

Calculate the time for the outbound trip.

1.25 hours

Time equals distance divided by speed (

15 \text{ miles} / 12 \text{ mph} = 1.25 \text{ hours}

).

2

Calculate the time for the return trip.

0.75 hours

Time equals distance divided by speed (

15 \text{ miles} / 20 \text{ mph} = 0.75 \text{ hours}

).

3

Determine the total time and total distance for the entire round trip.

Total time = 2 hours, Total distance = 30 miles

Adding the outbound and return times (

1.25 + 0.75

) gives 2 hours. The round trip is twice the one-way distance (

15 \times 2

).

4

Calculate the average speed for the entire round trip.

15 mph

Average speed is total distance divided by total time (

30 \text{ miles} / 2 \text{ hours} = 15 \text{ mph}

).

Key Concept

Average Speed for a Round Trip

Question 394Question →

A pilot flies a cargo plane from Airport A to Airport B at an average speed of $240$ mph. The pilot returns along the exact same route, but due to a strong headwind, the return flight averages only $160$ mph. If the total flying time for the entire round trip was exactly $5$ hours, what is the one-way distance between Airport A and Airport B, in miles?

Show answer & explanation

Answer: 480

Answer

480

By setting up an algebraic equation representing the total time taken for both legs of the trip (using Time = Distance / Speed), we get

d/240 + d/160 = 5

. Solving this equation by finding a common denominator of

480

yields

5d/480 = 5

, which simplifies to

d = 480

miles.

Step-by-Step Solution

1

Define a variable for the unknown distance.

Let

d

be the one-way distance in miles.

We need to find the one-way distance and relate it to the given times and speeds.

2

Express the time for each leg of the trip using the formula Time = Distance / Speed.

Outbound time =

\frac{d}{240}

, Return time =

\frac{d}{160}

.

The total time is given, so we need mathematical expressions for the time of each individual leg.

3

Set up an equation for the total time.

\frac{d}{240} + \frac{d}{160} = 5

The sum of the outbound flight time and the return flight time equals the total round-trip flight time.

4

Find a common denominator to add the fractions.

The least common multiple of

240

and

160

is

480

. The equation becomes

\frac{2d}{480} + \frac{3d}{480} = 5

.

To solve for

d

, we must combine the fractional terms into a single term.

5

Solve the equation for

d

.

\frac{5d}{480} = 5 \Rightarrow 5d = 2400 \Rightarrow d = 480

.

Isolating

d

gives the final one-way distance.

Key Concept

Solving round trip scenarios by setting up a total time equation:

\frac{d}{v_1} + \frac{d}{v_2} = t_{total}

Estimated Time:2m 0s

Question 395Question →

A city planner is designing a rectangular park that features a central grassy area measuring $150 \text{ feet}$ long and $90 \text{ feet}$ wide. A uniform concrete walkway that is $6 \text{ feet}$ wide will be constructed around the entire outer perimeter of the grassy area. If the concrete paving costs $\$12.50$ per square yard, what is the total cost, in dollars, of the paving material required for the walkway?

Show answer & explanation

Answer: 4200

Answer

4200

The correct cost is found by determining the total area of the walkway by subtracting the inner grass area from the outer total area (

16,524 - 13,500 = 3,024 \text{ sq ft}

), converting to square yards by dividing by 9 (

336 \text{ sq yd}

), and multiplying by the price of

\$12.50

per square yard.

Step-by-Step Solution

1

Determine the outer dimensions of the total area.

Outer length = 162 ft, Outer width = 102 ft.

The walkway is 6 feet wide and borders all sides. Therefore, 6 feet must be added to both ends of the length (

150 + 6 + 6 = 162

) and both sides of the width (

90 + 6 + 6 = 102

).

2

Calculate the area of the outer rectangle.

16,524 sq ft

Area is length multiplied by width:

162 \times 102 = 16,524

.

3

Calculate the area of the inner grassy rectangle.

13,500 sq ft

Using the given inner dimensions:

150 \times 90 = 13,500

.

4

Find the area of the walkway.

3,024 sq ft

Subtract the inner area from the outer area:

16,524 - 13,500 = 3,024

.

5

Convert the walkway area from square feet to square yards.

336 sq yd

There are

3 \times 3 = 9

square feet in one square yard. Divide the area by 9:

3,024 \div 9 = 336

.

6

Calculate the total cost.

$4,200

Multiply the area in square yards by the cost per square yard:

336 \times 12.50 = 4,200

.

Key Concept

Calculating subtractive rectangular area and converting square units for cost analysis.

Question 396Question →

A commercial painting crew is hired to paint the four exterior walls of a rectangular warehouse. The warehouse has a length of $120\text{ ft}$ , a width of $80\text{ ft}$ , and a height of $24\text{ ft}$ . The building features $2$ identical loading doors, each measuring $16\text{ ft}$ wide by $15\text{ ft}$ high, and $4$ identical windows, each measuring $6\text{ ft}$ wide by $5\text{ ft}$ high. The doors and windows will not be painted. The crew must apply exactly $2$ coats of paint to all paintable exterior wall surfaces. If one gallon of paint covers exactly $400\text{ square feet}$ , how many total gallons of paint are required for this project?

Show answer & explanation

Answer: 45

Answer

45

The total area of the four exterior walls is 9,600 sq ft. The doors and windows have a combined area of 600 sq ft, leaving a net paintable area of 9,000 sq ft per coat. Since two coats are required, the total area to cover is 18,000 sq ft. With each gallon covering 400 sq ft, dividing 18,000 by 400 gives exactly 45 gallons.

Step-by-Step Solution

1

Calculate the gross area of the four exterior walls.

9,600 sq ft

To find the total surface area before accounting for doors and windows.

2

Calculate the total area of the unpainted cutouts.

600 sq ft

The doors and windows will not be painted and must be subtracted.

3

Determine the net paintable area for a single coat.

9,000 sq ft

Subtracting the cutout area from the gross area gives the actual area to paint.

4

Calculate the total area to be covered for two coats.

18,000 sq ft

The problem specifies that exactly two coats of paint must be applied.

5

Determine the total gallons of paint required.

45

Divide the total area to be painted by the coverage rate of 400 sq ft per gallon.

Key Concept

Calculating net rectangular area by subtracting cutouts and applying a rate for multiple layers.

Question 397Question →

A military training exercise lasts for exactly 2 hours and 45 minutes. What is the total duration of the exercise in minutes?

Show answer & explanation

Answer: 165

Answer

165

The correct total is found by converting the 2 hours into 120 minutes and adding the extra 45 minutes, resulting in a total of 165 minutes.

Step-by-Step Solution

1

Convert the hours portion of the duration to minutes.

2 hours × 60 minutes/hour = 120 minutes.

Time is based on a base-60 system, meaning each hour contains exactly 60 minutes.

2

Add the remaining minutes to the converted hour total.

120 minutes + 45 minutes = 165 minutes.

To find the total duration in a single unit, all partial time units must be combined.

Key Concept

Converting mixed time units (hours and minutes) into a single unit (minutes).

Question 398Question →

A facility manager is replacing the flooring in a rectangular open-plan office that measures $60\text{ ft}$ in length and $46\text{ ft}$ in width. The office contains two identical rectangular utility columns, each measuring $6\text{ ft}$ by $5\text{ ft}$ , which will not be covered with the new flooring. If the new flooring material costs $\$22.00$ per square yard, what is the total cost of the flooring material required for the office in dollars?

Show answer & explanation

Answer: 6600

Answer

6600

The correct calculation correctly subtracts the area of the utility columns to find the net area in square feet, correctly converts this area to square yards by dividing by 9, and then multiplies by the price per square yard to find the final total cost.

Step-by-Step Solution

1

Calculate the gross area of the office.

2760 sq ft

The total rectangular area without accounting for the utility columns is

60 \times 46

.

2

Calculate the total area of the two utility columns.

60 sq ft

Each column is

6 \times 5 = 30\text{ sq ft}

, and there are two of them, so

30 \times 2 = 60\text{ sq ft}

.

3

Subtract the column area from the gross area.

2700 sq ft

This provides the net area that requires new flooring.

4

Convert the net area from square feet to square yards.

300 sq yd

The flooring cost is given per square yard, and there are

9\text{ sq ft}

in

1\text{ sq yd}

. Therefore,

2700 \div 9 = 300

.

5

Calculate the total cost of the flooring material.

6600

Multiply the area in square yards by the cost per square yard:

300 \times 22 = 6600

.

Key Concept

Calculating subtractive rectangular area and applying square unit conversions to determine total cost.

Question 399Question →

A military supply vehicle is equipped with tires that have a radius of $14$ inches. How many complete revolutions does each tire make if the vehicle travels a straight-line distance of $1.5$ miles? (Use $\pi = \frac{22}{7}$ and $1 \text{ mile} = 5,280 \text{ feet}$ .)

Show answer & explanation

Answer: 1080

Answer

1080

The total distance must be converted into inches (

1.5 \text{ miles} \times 5,280 \text{ ft/mile} \times 12 \text{ in/ft} = 95,040 \text{ inches}

). The tire's circumference (

2 \times \frac{22}{7} \times 14 = 88 \text{ inches}

) represents one revolution. Dividing the total distance by the circumference (

95,040 \div 88

) gives exactly

1,080

complete revolutions.

Step-by-Step Solution

1

Convert the total travel distance from miles to feet.

1.5 \times 5,280 = 7,920

feet

The distance must be in the same units as the tire measurements. It is easier to step down to feet first.

2

Convert the distance from feet to inches.

7,920 \times 12 = 95,040

inches

Since the tire radius is in inches, the total distance must also be in inches to calculate revolutions accurately.

3

Calculate the circumference of the tire.

C = 2 \times \pi \times r = 2 \times \frac{22}{7} \times 14 = 88

inches

One revolution of the tire equals its circumference, representing the distance traveled in a single rotation.

4

Calculate the total number of complete revolutions.

95,040 \div 88 = 1,080

revolutions

Dividing the total distance by the distance per revolution yields the total number of revolutions.

Key Concept

Calculating distance traveled using wheel revolutions requires relating linear distance to circular circumference, while ensuring all units of measurement are consistent.

Estimated Time:2m 0s

Question 400Question →

A business owner is paving a rectangular parking lot that measures $40\text{ feet}$ long and $30\text{ feet}$ wide. If the paving costs $\$5$ per square foot, what is the total cost of paving the lot in dollars?

Show answer & explanation

Answer: 6000

Answer

6000

The parking lot is a rectangle, so its area is found by multiplying the length by the width (

40 \times 30 = 1,200\text{ sq ft}

). Since the paving costs

\$5

for every square foot, the total cost is the area multiplied by the rate (

1,200 \times 5 = 6,000

). The final cost is

\$6,000

.

Step-by-Step Solution

1

Calculate the total area of the rectangular parking lot.

1,200 square feet

The total area is required to know how many square feet need to be paved.

2

Multiply the calculated area by the cost per square foot.

6,000

Each of the 1,200 square feet costs $5 to pave, so multiplying them gives the total cost.

Key Concept

Calculating the area of a rectangle and applying it to find the total cost of materials or services.

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