A supply convoy is scheduled to travel a total distance of 135 miles to a forward operatin… — Armed Services Vocational Aptitude Battery (ASVAB)

A supply convoy is scheduled to travel a total distance of $135$ miles to a forward operating base in exactly $3$ hours and $30$ minutes. For the first $90$ minutes, the convoy travels along a secured highway at an average rate of $50$ miles per hour. For the remainder of the route, what must be the convoy's average rate of speed, in miles per hour, to arrive exactly on time?

Cevap: 30 mph

Cevap

The convoy must cover the remaining

60

miles in the remaining

2.0

hours, which requires an average speed of

30

miles per hour.

Adım Adım Çözüm

Convert the given travel times from minutes to hours.

3

hours and

30

minutes =

3.5

hours.

90

minutes =

1.5

hours.

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

Calculate the distance covered on the secured highway.

50 \text{ miles/hour} \times 1.5 \text{ hours} = 75 \text{ miles}

To find out how much of the total distance has already been traveled.

Calculate the remaining distance to the forward operating base.

135 \text{ miles} - 75 \text{ miles} = 60 \text{ miles}

This is the distance that must be covered during the off-road portion of the route.

Calculate the remaining travel time available.

3.5 \text{ hours} - 1.5 \text{ hours} = 2.0 \text{ hours}

This is the time limit for completing the rest of the journey.

Calculate the required average speed for the remaining distance.

60 \text{ miles} \div 2.0 \text{ hours} = 30 \text{ miles per hour}

Rate equals distance divided by time (

r = \frac{d}{t}

Anahtar Kavram

Calculating Rate and Time

Alternatif Yöntem

You could set up an algebraic equation for the total distance:

(50 \times 1.5) + (r \times 2.0) = 135

. Solving for

r

75 + 2r = 135

, so

2r = 60

, which means

r = 30

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

Konular

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