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 same distance than for the motorcycle. How long does it take them to meet, if they start moving towards each other simultaneously?

Answer 1

A motorcycle will complete the 540 mile trip in
`(540)/(48) = 11.25 hr`

And the car will complete it 2.25 hours less, i.e 11.25 -2,25 = 9 hours.

then,

Speed of the car is
`(540)/(9) = 60 km/hr`

60t + 48t = 540

108t = 540

Divide both sides by 108 we get

t = 5

So, they will meet in 5 hours,

After 5 hours, the motorcycle will have traveled
`48 * 5 = 240 miles`

and the car will have traveled =
`60 * 5 = 300 miles`

Answer 2

Given is :

The distance between the cities Chicago and Toronto is = 540 miles

Speed of motorcycle = 48 mph

So, time taken by motorcycle to cover 540 miles =
`(540)/(48)=11.25` hours

Hence, the motorcycle will complete the 540 miles trip in 11.25 hours.

As given, the car takes 2.25 hours less to cover the same distance, so car takes
`11.25-2.25=9` hours

So,the speed of the car therefore is
`(540)/(9)=60` mph.

Let both the car and motorcycle meets is 't' time.

So,
`60t+48t=540`

`108t=540`

t = 5

So, they will meet in 5 hours.

After 5 hours, the motorcycle will have traveled 48x5 = 240 miles

And the car will have traveled 60x5 = 300 miles.