Atruck enters a highway driving 60 mph. a car enters the highway at the same place 13 minutes later and drives 75 mph in the same direction. from the time the car enters the highway, how long will it take the car to pass the truck?

Given: A truck enters a highway driving 60 mph.

A car enters the highway at the same place 13 minutes later and drives 75 mph in the same direction.

Let the truck covers 'x' m distance in time 't' hour the car will take [t -(13 /60)] hour to cover the same distance 'x'

Concept:    Distance = Speed × Time

For Truck:       Distance (x) =  60 mph × t    (i)

For Car:          Distance (x) =  75 mph × [t -(13 /60)] (ii)

From equations (i) and (ii)

                      75 mph × [t -(13 /60)] =  60 mph × t  

or,                   75 mph × t -75×(13 /60) =  60 mph × t  

or,                75 mph × t -  60 mph × t  = 75×(13 /60)    

or,                                       15 mph × t  = 75×(13 /60)

or,                                                       t  = 75×13 / (15×60) h

or,                                                       t  ≈ 1.08 h = 64.999 minutes

Therefore, the car will cover the same distance in 64.999 - 13 = 51.999 minutes ≈ 52 minutes

Hence, the car will pass the truck after 52 minutes after its starting the race.