Precalculus word problem

Question

a truck enters a highway driving 60 mph. a car enters the highway at the same place 9 minutes later and drives 74 mph in the same direction. from the time the car enters the highway, how long will it take the car to pass the truck?

Answer 1

another way to think of this is to use the distance equation

Distance = rate X time

Since the car and truck enter highway at the same place at the time the car catches up to truck they will have traveled equal distances.

We know the truck starts 9 minutes before the car which will mean it will have traveled 9 more minutes than the car at the time they catch up

Let t = time car travels

t + 9 = time truck travels

so for car d = 60 (t + 9)

for truck d = 74 t

By substitution,

60 (t + 9) = 74 t

60t +540 = 74 t

540 = 14 t

t = 38.57 minutes

Answer 2

The car gains 14 mph, which is (14/60) = (7/30) = 0.2333... miles per minute, and has an initial deficit of 9 minutes. From this it follows that it takes the car 9/0.23333... = 38.57 minutes, or (38 and 5/7ths, to be precise) minutes to catch up.