An engineer battalion is transporting heavy equipment in a convoy to a forward operating b… — Armed Services Vocational Aptitude Battery (ASVAB)

An engineer battalion is transporting heavy equipment in a convoy to a forward operating base $210$ miles away. To arrive on schedule, the convoy must maintain an overall average speed of $42$ mph for the entire journey.

During the first leg, the convoy travels $120$ miles in $2$ hours. They then halt for $30$ minutes to inspect the equipment.

What average speed must the convoy maintain for the remainder of the trip to achieve the target overall average speed?

A
24 mph
B
30 mph
36 mphAnswer
D
60 mph

Answer

The convoy must maintain an average speed of 36 mph for the remainder of the trip.

To achieve an overall average speed of

42

mph over

210

miles, the total journey must take exactly

5

hours. The convoy has already used

2.5

hours (

2

hours driving +

0.5

hours resting) and covered

120

miles. This leaves

90

miles to be covered in the remaining

2.5

hours. Dividing the remaining distance by the remaining time (

90 / 2.5

) gives the required speed of

36

mph.

Step-by-Step Solution

Calculate the total time required for the entire journey.

Total Time =

210 \text{ miles} / 42 \text{ mph} = 5 \text{ hours}

To find the time available for the second leg, we first need to know the total time allowed for the mission.

Calculate the time spent on the first leg and the rest stop.

Time Spent =

2 \text{ hours} + 30 \text{ minutes} = 2.5 \text{ hours}

The rest stop must be included in the total elapsed time because the overall average speed accounts for the entire duration of the journey.

Determine the remaining distance and remaining time for the final leg.

Remaining Distance =

210 - 120 = 90 \text{ miles}

.
Remaining Time =

5 - 2.5 = 2.5 \text{ hours}

Subtracting the distance already covered and the time already spent gives the parameters for the final segment.

Calculate the required average speed for the final leg.

Speed =

90 \text{ miles} / 2.5 \text{ hours} = 36 \text{ mph}

Average speed is always calculated as total distance divided by total time for that specific segment.

Key Concept

To find a missing speed in a multi-leg journey, use the total distance and target average speed to find the total allowed time. Subtract the time and distance already used (including rest stops) to find the parameters for the remaining leg.

Alternative Method

You can work entirely in minutes to avoid decimals. Total time is

300

minutes. Time spent is

150

minutes. Time remaining is

150

minutes. Speed needed is

90 \text{ miles} / 150 \text{ minutes} = 0.6 \text{ miles per minute}

. Multiply by

60

to convert to

36

mph.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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