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 will take them 5 hours to meet if they start moving towards eachother simultaneusly.

Explanation:

Distance, s = 540 miles

Motocycle's speed, v = 48 mph

Time for motorcycle to cover 48 miles, t =
`(Distance)/(Speed)`

=
`(540)/(48)` = 11.25 h

For a car it takes 2.25 hours less than 11.25 for motorcycle:

Time for car than becomes: 11.25 - 2.25 = 9 h

Speed for car would be v(c) =
`(Distance)/(Time)`

=
`(540)/(9)` = 60 mph

For finding when they will meet, we will need relative speed:

Since they are moving towards each other the relative speed is the sum of speed of car and the speed of motorcycle

Relative Speed = 48 + 60 = 108 mph

Distance = 540 miles

Time =
`(Distance)/(Speed)`

=
`(540)/(108)`

= 5 hours