Question

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. from the time the car enters the​ highway, how long will it take the car to pass the​ truck?

Answer 1

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.