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?

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

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.