A military transport convoy departs from a base and travels on a straight route at a const… — Armed Services Vocational Aptitude Battery (ASVAB)

A military transport convoy departs from a base and travels on a straight route at a constant speed of $30$ mph. Exactly $15$ minutes later, a tactical vehicle is dispatched along the same route to deliver updated orders, traveling at a constant speed of $45$ mph. How many minutes will it take for the tactical vehicle to catch up to the convoy from the time the tactical vehicle departs?

A
6
B
60
30Cevap
D
300

Cevap

The correct answer accurately calculates the

7.5

-mile head start distance (

30 \text{ mph} \times 0.25 \text{ hours}

) and divides it by the

15

mph relative speed (

45 \text{ mph} - 30 \text{ mph}

) to find a catch-up time of

0.5

hours, which equals

30

minutes.

Adım Adım Çözüm

Convert the convoy's head start time from minutes to hours.

15 \text{ minutes} = 0.25 \text{ hours}

Vehicle speeds are given in miles per hour (mph), so the time must be converted to hours for unit consistency.

Calculate the distance the convoy traveled during its head start.

30 \text{ mph} \times 0.25 \text{ hours} = 7.5 \text{ miles}

This establishes the initial distance gap that the tactical vehicle needs to close.

Determine the relative catch-up speed of the tactical vehicle.

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

Because the vehicles are traveling in the same direction, you subtract the slower speed from the faster speed to find the rate at which the gap is closing.

Calculate the time required to close the gap in hours.

7.5 \text{ miles} \div 15 \text{ mph} = 0.5 \text{ hours}

Time equals distance divided by rate (

t = \frac{d}{r}

Convert the catch-up time back to minutes.

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

The question specifically asks for the time in minutes.

Anahtar Kavram

Catch-up scenarios require calculating the initial distance gap and dividing it by the relative speed (the difference in speeds) between the two moving objects.

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