Calculating Distance Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 2

Question 21Question →

A logistics convoy leaves a supply depot and travels at a steady speed of 40 miles per hour for 2 hours and 15 minutes. After a 45-minute halt to refuel, the convoy resumes its route at a speed that is 20% faster than its initial speed. It travels at this new speed for 1 hour and 40 minutes until reaching the forward operating base. What is the total distance traveled by the convoy, in miles?

Show answer & explanation

Answer: 170; 170 miles; 170 mi

Answer

170

The correct answer is found by breaking the journey into two separate legs of movement, converting all times to hours, calculating the distance for each leg independently using their respective speeds, and summing the results.

Step-by-Step Solution

1

Calculate the time traveled during the first leg in hours.

2 hours and 15 minutes is equivalent to 2.25 hours.

Since the speed is given in miles per hour, time must be expressed in hours.

2

Calculate the distance covered during the first leg.

40 mph × 2.25 hours = 90 miles.

Using the distance formula

d = r \times t

.

3

Determine the speed of the convoy for the second leg.

40 mph + (0.20 × 40 mph) = 40 + 8 = 48 mph.

The problem states the convoy travels 20% faster after the halt.

4

Calculate the time traveled during the second leg in hours.

1 hour and 40 minutes is equivalent to

1 \frac{40}{60}

hours, which simplifies to

\frac{5}{3}

hours.

Converting mixed time units to a single fraction of hours is necessary for accurate calculation.

5

Calculate the distance covered during the second leg.

48 mph ×

\frac{5}{3}

hours = 80 miles.

Using the distance formula

d = r \times t

.

6

Calculate the total distance traveled.

90 miles + 80 miles = 170 miles.

The total distance is the sum of the distances from the two active travel legs. The 45-minute halt added 0 miles.

Key Concept

Calculating distance across multiple legs with varying speeds and mixed time units.

Question 22Question →

A military cargo plane flies for $2$ hours and $20$ minutes at an average speed of $420$ miles per hour. It then encounters a strong headwind, reducing its average speed to $360$ miles per hour for the remaining $45$ minutes of the flight. What is the total distance, in miles, traveled by the cargo plane?

Show answer & explanation

Answer: 1250; 1250 miles; 1,250; 1,250 miles

Answer

The total distance traveled by the cargo plane is 1250 miles.

The problem requires calculating the distance for two separate flight segments and adding them together. For the first segment, the time is

2

hours and

20

minutes (

\frac{7}{3}

hours) and the speed is

420

mph, resulting in

980

miles. For the second segment, the time is

45

minutes (

\frac{3}{4}

hours) and the speed is

360

mph, resulting in

270

miles. Adding these distances yields a total of

1250

miles.

Step-by-Step Solution

1

Convert the flight time of the first leg into hours.

2

hours and

20

minutes is equal to

2\frac{1}{3}

hours, or

\frac{7}{3}

hours.

Speed is given in miles per hour, so time must be in hours to correctly use the distance formula.

2

Calculate the distance traveled during the first leg.

420 \times \frac{7}{3} = 980

miles.

Applying the formula Distance = Rate

\times

Time.

3

Convert the flight time of the second leg into hours.

45

minutes is equal to

\frac{45}{60}

hours, which simplifies to

\frac{3}{4}

hours.

Uniform units are required before calculating the distance for the second segment.

4

Calculate the distance traveled during the second leg.

360 \times \frac{3}{4} = 270

miles.

Applying the formula Distance = Rate

\times

Time for the reduced speed segment.

5

Add the distances from both legs to find the total distance.

980 + 270 = 1250

miles.

The total distance is the sum of the distances traveled in each individual segment of the flight.

Key Concept

Calculating total distance for a multi-leg journey by accurately converting minutes to fractional hours and applying the Distance = Rate

\times

Time formula.

Question 23Question →

A high-speed passenger train travels between two major cities. It covers the first segment of the journey at an average speed of $120\text{ mph}$ for $1\text{ hour and } 45\text{ minutes}$ . Due to track maintenance, it reduces its speed to $40\text{ mph}$ for $36\text{ minutes}$ . After clearing the maintenance zone, it accelerates and travels at $150\text{ mph}$ for $48\text{ minutes}$ to reach its final destination. What is the total distance of the trip?

354 miles

260.4 miles

325.5 miles

330 miles

Show answer & explanation

Answer: 354 miles

Answer

354 miles

The total distance is found by calculating the distance of each leg separately and adding them together. First, convert all minute values into hours by dividing by 60 (

1\text{ hr } 45\text{ min} = 1.75\text{ hr}

;

36\text{ min} = 0.6\text{ hr}

;

48\text{ min} = 0.8\text{ hr}

). Then, multiply each time by its corresponding speed to find the distances:

120 \times 1.75 = 210\text{ miles}

;

40 \times 0.6 = 24\text{ miles}

; and

150 \times 0.8 = 120\text{ miles}

. Adding these together gives

210 + 24 + 120 = 354\text{ miles}

.

Step-by-Step Solution

1

Convert the travel time for the first segment into hours.

45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}

. Total time

= 1.75\text{ hours}

.

Speed is given in miles per hour (mph), so time must be in hours to calculate distance correctly.

2

Calculate the distance covered in the first segment.

Distance

= 120\text{ mph} \times 1.75\text{ hours} = 210\text{ miles}

.

Applying the formula Distance = Rate × Time for the first leg of the journey.

3

Convert the time and calculate the distance for the second (maintenance) segment.

Time

= \frac{36}{60}\text{ hours} = 0.6\text{ hours}

. Distance

= 40\text{ mph} \times 0.6\text{ hours} = 24\text{ miles}

.

The second segment has a different speed and time that must be evaluated independently.

4

Convert the time and calculate the distance for the final segment.

Time

= \frac{48}{60}\text{ hours} = 0.8\text{ hours}

. Distance

= 150\text{ mph} \times 0.8\text{ hours} = 120\text{ miles}

.

The final segment has its own rate and duration to calculate.

5

Sum the distances of all segments to find the total distance.

210 + 24 + 120 = 354\text{ miles}

.

The total distance of a multi-leg journey is the sum of the distances of the individual legs.

Key Concept

Calculating distance using mixed time units across multiple journey segments

Question 24Question →

A Coast Guard search-and-rescue aircraft executes a mission over the ocean. It first flies directly to the designated search zone at an average speed of $180\text{ mph}$ for $1$ hour and $20$ minutes. Once inside the zone, it slows to a search speed of $120\text{ mph}$ , flying a grid pattern for $2$ hours and $15$ minutes. After completing the grid, it returns to base along a direct route at $150\text{ mph}$ for $48$ minutes. What is the total distance flown by the aircraft during the entire mission, in miles?

Show answer & explanation

Answer: 630

Answer

630

The correct total distance is 630 miles. This is found by carefully converting the travel times of all three mission legs into hours, calculating the distance for each leg using the formula Distance = Rate × Time, and then summing the three results together.

Step-by-Step Solution

1

Calculate the distance flown to reach the search zone.

180 mph * (4/3) hours = 240 miles.

Converting 1 hour and 20 minutes to 1.333... (or 4/3) hours is required to match the speed unit (mph).

2

Calculate the distance flown while searching the grid.

120 mph * 2.25 hours = 270 miles.

Converting 2 hours and 15 minutes to 2.25 hours is required to match the speed unit (mph).

3

Calculate the distance flown to return to base.

150 mph * 0.8 hours = 120 miles.

Converting 48 minutes to 48/60 or 0.8 hours is required to match the speed unit (mph).

4

Sum the distances from all three legs of the mission.

240 + 270 + 120 = 630 miles.

The total distance is the sum of the individual leg distances.

Key Concept

Calculating distance for multiple travel segments by independently converting mixed time units into hours and applying the Distance = Rate × Time formula.

Estimated Time:2m 30s

Calculating Distance

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