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A car travels 120 miles in the same amount of time that it takes a truck to travel 100 miles. The car travels 10 miles per hour faster than the truck. True or false?

User Alesss
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1 Answer

6 votes

Answer:

The affirmation is only true if the truck is traveling at 50 mi/h.

Step-by-step explanation:

Hi there!

Let´s use the equation of average velocity (AV) to solve this problem:

AV = Δx / t

Where:

Δx = traveled distance.

t = time.

For the car, its average velocity (vc) will be:

vc = 120 miles / t

For the truck:

vtr = 100 miles / t

If we solve both equations for t and then equalize them (since the time is the same for both vehicles):

vc = 120 miles / t

t = 120 mi / vc

vtr = 100 miles / t

t = 100 mi / vtr

120 mi / vc = 100 mi / vtr

multiply both sides by vc and divide by 100:

120 mi / 100 mi = vc / vtr

1.2 = vc / vtr

1.2 · vtr = vc

The car travels 1.2 times faster than the truck.

Let´s see at which velocity of the truck, the car is traveling 10 mi/h faster. In this case, vc = 10 mi/h + vtr:

1.2 · vtr = 10 mi/h + vtr

1.2 vtr - vtr = 10 mi/h

0.2 vtr = 10 mi/h

vtr = 10 mi/h / 0.2

vtr = 50 mi/h

The affirmation is only true if the truck is traveling at 50 mi/h.

User Mrmar
by
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