Question

The distance between the cities Chicago and Toronto is 540 miles. A motorcycle's speed is 48 mph. For a car, it takes 2.25 hours less to cover the same distance than for the motorcycle. How long does it take them to meet, if they start moving towards each other simultaneously?

The answer is in hours.

PLEASE HELP ME

Answer 1

5 hours

Explanation:

given :

Distance between the cities = 540 miles

Speed of motorcycle =48 mph

TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :

`(DISTANCE)/(SPEED)`

By putting given values in the formula we get :

`(540)/(48)`

= 11.25 hours

Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle

⇒ 11.25 hours - 2.25 hours

⇒ 9 hours

Thus , Time taken by car to cover the same distance is 9 hours .

Now to calculate speed of car by using formula:

`(distance)/(time)`

`(540)/(9)`

= 60 mph

Let t be the time taken to meet if they start moving towards each other.

So distance covered by motorcycle in t hours is

speed\times time

= 48t miles

Distance covered by car in t hours is

speed\times time

= 60t miles

⇒ 60t + 48t =540

⇒ 108t = 540

⇒ t= 5 hours

Therefore, time taken to meet if they start moving towards each other is 5 hours.