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

Explanation:

let they travel the distance between them alone

d = common distance traveled by both motorcycle and car = 540 miles

`t_(m)`= time taken by motorcycle to travel distance between them

`v_(m)` = speed of the motorcycle = 48 mph

time taken by motorcycle to travel distance between them is given as

`t_(m)`= d/
`v_(m)`

`t_(m)`=540/48

`t_(m)`= 11.25 h

`t_(c)`= time taken by car to travel distance "d" =11.25 - 2.25 = 9 h

`v_(m)` = speed of the motorcycle

speed of motorcycle is given as

`v_(m)` = d/
`t_(m)`

`v_(m)` = 540/9

`v_(m)` = 60 mph

when the car and motorcycle move towards each other, the relative speed is given as

v =
`v_(m)` +
`v_(c)`

v = 60 + 48

v = 108 mph

t = time taken to meet

Time taken to meet is given as

t = d/v

t = 540/108

t = 5 h