Question

A truck enters a highway driving 60 miles per hour a car enters the highway at the same place 9 minutes later and drive 68 miles per hour 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

The time taken by car to pass the truck is 1.125 hours

Solution:

A truck enters a highway driving 60 miles per hour a car

The car enters the highway at the same place 9 minutes later and drive 68 miles per hour in the same direction from the time the car enters the highway

Let us first convert 9 minutes to hours

$1 \text{ minute } = \frac{1}{60} \text{ hour }$

$9 \text{ minute } = \frac{9}{60} = \frac{3}{20} \text{ hours }$

Let the truck covers 'x' m distance in time 't' hour the car will take [t -(3/20)] hour to cover the same distance 'x'

We know that,

$Distance = Speed \times Time$

For truck : $x = 60t$ ----------- eqn 1

For car: $x = 68 \times (t - \frac{3}{20})$ ------------ eqn 2

From equations (i) and (ii)

$60t = 68 \times(t-\frac{3}{20})\\\\60t = 68t-10.2\\\\68t - 60t = 10.2\\\\8t = 10.2\\\\t = 1.275$

Thus the time taken by car to pass the truck is:$t - \frac{3}{20} = 1.275 - \frac{3}{20} = 1.275 - 0.15 = 1.125$

Thus the time taken by car to pass the truck is 1.125 hours