Time, Rate, and Distance Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 6

Soru 101Soru →

A naval supply ship leaves port heading due east at a constant speed of $24$ knots. Exactly $1$ hour and $45$ minutes later, a destroyer leaves the same port to intercept the supply ship, traveling on the exact same course at a constant speed of $36$ knots. How many hours will it take for the destroyer to catch up with the supply ship, measured from the moment the destroyer leaves port?

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Cevap: 3.5; 3.5 hours; 3 1/2; 3 1/2 hours; 3.5 hrs; 7/2

Cevap

3.5

The destroyer must close an initial gap of

42

nautical miles. Since it travels

12

knots faster than the supply ship, it closes the gap at a relative rate of

12

knots, which takes exactly

3.5

hours.

Adım Adım Çözüm

1

Convert the head start time from hours and minutes into a decimal or fraction of hours.

1

hour and

45

minutes =

1.75

hours (or

\frac{7}{4}

hours).

Time units must properly match the speed units (knots, which are nautical miles per hour) before calculating distance.

2

Calculate the distance the supply ship traveled during its head start.

24 \text{ knots} \times 1.75 \text{ hours} = 42 \text{ nautical miles}

.

This establishes the initial gap distance the destroyer needs to close.

3

Determine the relative speed at which the destroyer is closing the gap.

36 \text{ knots} - 24 \text{ knots} = 12 \text{ knots}

.

Because both ships are traveling in the same direction, you subtract the slower speed from the faster speed to find the catch-up rate.

4

Calculate the time required to close the gap.

\frac{42 \text{ nautical miles}}{12 \text{ knots}} = 3.5 \text{ hours}

.

Time equals distance divided by rate. The gap distance divided by the relative speed gives the exact time to intercept.

Anahtar Kavram

Relative Motion and Catch-Up Scenarios

Soru 102Soru →

A commercial cargo flight leaves an airport at 06:00 AM, heading due east at a constant cruising speed of $300$ mph. At 07:30 AM, a passenger jet leaves the same airport, flying along the exact same route at a constant cruising speed of $600$ mph. At what time will the passenger jet catch up to the cargo flight?

08:00 AM

08:30 AM

09:00 AM

09:20 AM

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Cevap: 09:00 AM

Cevap

09:00 AM

The cargo flight has a

1.5

-hour head start, covering

450

miles (

300 \text{ mph} \times 1.5 \text{ hours}

). Because both aircraft are traveling in the same direction, the passenger jet closes this gap at a relative speed of

300

mph (

600 \text{ mph} - 300 \text{ mph}

). It takes the passenger jet

1.5

hours to close the

450

-mile gap (

450 \div 300 = 1.5

). Adding

1.5

hours (

1

hour and

30

minutes) to the passenger jet's departure time of 07:30 AM gives a final catch-up time of 09:00 AM.

Adım Adım Çözüm

1

Calculate the time difference between the departures.

1.5

hours.

From 06:00 AM to 07:30 AM is exactly

1

hour and

30

minutes, or

1.5

hours. This determines how long the cargo flight traveled before the passenger jet departed.

2

Calculate the head-start distance of the cargo flight.

450

miles.

Using Distance = Rate

\times

Time, multiply the cargo flight's speed by its head-start time:

300 \text{ mph} \times 1.5 \text{ hours} = 450 \text{ miles}

.

3

Determine the relative speed of the two aircraft.

300

mph.

Because both aircraft are traveling in the same direction, subtract the slower speed from the faster speed to find how quickly the gap is closing:

600 \text{ mph} - 300 \text{ mph} = 300 \text{ mph}

.

4

Calculate the time required for the passenger jet to catch up.

1.5

hours.

Divide the head-start distance by the relative speed:

450 \text{ miles} \div 300 \text{ mph} = 1.5 \text{ hours}

.

5

Add the catch-up time to the passenger jet's departure time.

09:00 AM.

1.5

hours is

1

hour and

30

minutes. Adding this to 07:30 AM gives 09:00 AM.

Anahtar Kavram

Relative Motion (Same Direction)

Soru 103Soru →

A naval submarine is traveling underwater at a constant speed of $20\text{ feet per second}$ . At this rate, how many miles will the submarine travel in exactly $1\text{ hour}$ and $6\text{ minutes}$ ?

(Note: $1\text{ mile} = 5,280\text{ feet}$ )

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Cevap: 15

Cevap

15

First, the rate is given as 20 feet per second. The total time must be converted entirely to seconds: 1 hour and 6 minutes equals 66 minutes. Multiplying 66 minutes by 60 seconds per minute gives 3,960 seconds. Next, use the formula Distance = Rate × Time to find the distance in feet: 20 × 3,960 = 79,200 feet. Finally, convert this distance into miles by dividing by 5,280. 79,200 ÷ 5,280 = 15 miles.

Adım Adım Çözüm

1

Convert the total travel time into seconds to match the unit of the given speed.

The total time is 3,960 seconds.

Rates and times must share the same time unit before multiplying.

2

Calculate the total distance traveled in feet by multiplying the speed by the time in seconds.

The distance is 79,200 feet.

Distance equals rate multiplied by time (d = r * t).

3

Convert the distance from feet into miles by dividing by 5,280.

The final distance is 15 miles.

The question asks for the final answer in miles, and there are 5,280 feet in one mile.

Anahtar Kavram

Converting between multiple units of time and distance to solve for a missing variable in the distance formula.

Soru 104Soru →

A military supply convoy travels from Base Alpha to Base Bravo, a distance of 180 miles, and then returns along the exact same route. Fully loaded on the outbound trip, the convoy vehicles average 12 miles per gallon (MPG). Empty on the return trip, they average 15 MPG. If standard diesel fuel costs $4.00 per gallon, what is the total cost of fuel consumed by one vehicle for the entire round trip?

$108.00

$60.00

$6.75

$10.80

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Cevap: $108.00

Cevap

The total cost of fuel for the round trip is $108.00.

The correct answer accurately determines the total fuel by breaking the round trip into two separate legs with different efficiencies. The outbound leg requires 15 gallons (180 / 12) and the return leg requires 12 gallons (180 / 15), for a total of 27 gallons. Multiplying this total by the

4.00 price per gallon yields

108.00.

Adım Adım Çözüm

1

Calculate the fuel consumed on the outbound trip.

180 miles / 12 MPG = 15 gallons

Dividing distance by fuel efficiency gives the amount of fuel used for the first leg.

2

Calculate the fuel consumed on the return trip.

180 miles / 15 MPG = 12 gallons

The return trip covers the same distance but at a different fuel efficiency because the vehicle is empty.

3

Determine the total amount of fuel consumed for the entire round trip.

15 gallons + 12 gallons = 27 gallons

Adding the fuel from both legs gives the total fuel requirement.

4

Calculate the total cost of the fuel.

27 gallons *

4.00/gallon =

108.00

Multiplying the total gallons used by the price per gallon yields the final cost.

Anahtar Kavram

Multi-step fuel efficiency and round-trip cost calculation.

Soru 105Soru →

Match each vehicle scenario to its calculated maximum usable travel range in miles.

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Cevap

The correct matches are: Delivery Truck corresponds to 608 miles, Patrol Boat corresponds to 576 miles, Light Aircraft corresponds to 590 miles, and Recreational Vehicle corresponds to 624 miles.

Each vehicle's range is properly determined by finding the product of its available fuel and fuel efficiency rate for each specific segment of travel, ensuring reserves and phase-specific rates are accurately applied.

Adım Adım Çözüm

1

Calculate the maximum range for the Delivery Truck.

City range is

288

miles and highway range is

320

miles, yielding a total of

608

miles.

Efficiency varies by driving condition, so total range is the sum of the calculated ranges for each proportional fuel segment.

2

Calculate the maximum range for the Patrol Boat.

Usable fuel is

96

gallons, yielding a range of

576

miles.

The

20\%

mandatory reserve cannot be used for the travel range calculation, meaning only

80\%

of the tank is available.

3

Calculate the maximum range for the Light Aircraft.

Remaining fuel is

270

gallons providing a cruise range of

540

miles. Adding the initial

50

miles yields

590

miles.

Total range includes both the ascent distance and the subsequent cruise distance.

4

Calculate the maximum range for the Recreational Vehicle.

Efficiency is

12

mpg, leading to a maximum range of

624

miles on a

52

-gallon tank.

The efficiency rate is constant, so it is derived from the prior trip and applied to the new full tank.

Anahtar Kavram

Calculating maximum range by determining usable fuel volumes and applying multiple rates of efficiency.

Soru 106Soru →

Match each vehicle's travel scenario with its calculated average speed in miles per hour (mph).

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Cevap

Match the scenarios to their respective speeds by converting all times strictly into hours, then dividing the distance by that time.

Each correct speed is found by converting the travel time into decimal or fractional hours and then properly applying the standard rate formula (

r = d/t

).

Adım Adım Çözüm

1

Convert the travel time in each scenario to hours.

Boat: 13/6 hours. Convoy: 2.8 hours. Train: 2.25 hours. Aircraft: 2.4 hours.

Because the required speed is in miles per hour (mph), the units of time must be strictly in hours.

2

Apply the speed formula: Rate = Distance / Time.

Boat: 65 / (13/6) = 30 mph. Convoy: 112 / 2.8 = 40 mph. Train: 135 / 2.25 = 60 mph. Aircraft: 384 / 2.4 = 160 mph.

Dividing the given distance in miles by the correct time in hours yields the average speed.

Anahtar Kavram

Calculating Rate and Time

Tahmini Süre:2m 30s

Time, Rate, and Distance

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