On a two lane highway, a car is following a pickup truck. At one instant, the car has a speed of 32 m/s and is 184 m behind the truck. At the same time, the truck has a speed of 28 m/s. If neither vehicle accelerates, how long will it take the car to catch up to the truck?
A)4.8 s
B)24 s
C)46 s
D)82 s
E)96 s

Question

Quizplus · Accepted Answer

Let's define the variables:

v_car = 32 m/s : speed of the car
v_truck = 28 m/s : speed of the truck
d0 = 184 m : initial distance between the car and the truck
t = ? : time for the car to catch up

We know that the distance between the car and the truck at any time t is:

d_car_truck = d0 + (v_car - v_truck) * t

When the car catches up to the truck, they will be at the same distance. Thus:

d_car_truck = 0

We can solve for t:

d0 + (v_car - v_truck) * t = 0
t = -d0 / (v_car - v_truck) = 46 s

Note that the negative sign in the equation simply means that the car catches up after a time corresponding to a positive value of t.

On a Two Lane Highway, a Car Is Following a Pickup