An armored vehicle traverses an 18-mile desert route. It travels the first 10 miles at a c… — Armed Services Vocational Aptitude Battery (ASVAB)

An armored vehicle traverses an $18$ -mile desert route. It travels the first $10$ miles at a constant speed of $20$ miles per hour. If the vehicle completes the entire route in exactly $45$ minutes, what is its speed in miles per hour for the remaining distance?

Answer: 32 mph

Answer

The speed for the remaining distance is

32

miles per hour.

To find the unknown speed, you must isolate the distance and time for the final segment. First, the time for the

10

-mile stretch is calculated as

0.5

hours, which is equivalent to

30

minutes. Subtracting this from the total

45

minutes leaves

15

minutes (or

0.25

hours) to travel the remaining

8

miles. Dividing the

8

miles by the

0.25

hours of remaining time yields a final speed of

32

miles per hour.

Step-by-Step Solution

Calculate the time for the first segment.

10 \text{ miles} \div 20 \text{ mph} = 0.5 \text{ hours}

You need to know how much time was spent on the first segment to determine the time left for the remainder of the route.

Convert the first segment's time into minutes.

0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}

The total time is provided in minutes (

45

minutes), so making the units consistent allows you to easily subtract and find the remaining time.

Find the remaining time available.

45 \text{ minutes} - 30 \text{ minutes} = 15 \text{ minutes}

This step determines exactly how much time the vehicle has to complete the rest of the route.

Convert the remaining time into hours.

15 \text{ minutes} \div 60 \text{ minutes/hour} = 0.25 \text{ hours}

Since the requested final speed must be in miles per hour, the time value needs to be expressed in hours.

Determine the remaining distance.

18 \text{ miles} - 10 \text{ miles} = 8 \text{ miles}

This is the physical distance the vehicle must cover during the final

15

minutes.

Calculate the speed for the final segment.

8 \text{ miles} \div 0.25 \text{ hours} = 32 \text{ mph}

Dividing the remaining distance by the remaining time gives the required speed.

Key Concept

Calculating unknown rates in multi-part trips by finding intermediate distances and times, and converting units correctly.

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