Question

The distance between the cities Atlanta and Indianapolis 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

it takes 5 hours to meet car and motorcycle heading towards each other.

Explanation:

We have given ,

Distance between two cities = 540 miles

Speed of a motorcycle = 48 mph

Then, time taken by motorcycle to cover the distance =
`(Distance)/(Speed)`

or , Time taken =
`(540)/(48)` = 11.25 hours

For a car it takes 2.25 hours less to cover same distance.

i.e time taken by car to cover same distance = 11.25 - 2.25 = 9 hours

So, the speed of car =
`(Distance)/(time)` = 540÷9 = 60 mph

i.e speed of car = 60 mph

No, we need to find the time taken by car and motorcycle if they start moving towards each other.

Since they are heading towards each other, speed of car and motorcycle will be added.

i,e Time taken = Total distance ÷ (Speed of car + Speed of motorcycle)

Time taken =
`(540)/(60+48)`

Time taken = 5 hours

Hence , it takes 5 hours to meet car and motorcycle heading towards each other.