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.