Question

5

An athlete covers three consecutive miles by walking the first mile, running the second mile

and cycling the third. He runs twice as fast as he walks, and he cycles one and a half times as

ast as he runs. He takes ten minutes longer than he would do if he cycled the three miles,

How long does he take by walking, running and cycling?

ter your math answer

Answer 1

Total time taken by walking, running and cycling = 22 minutes.

Explanation:

Let the speed of walking = x

As given,

The distance of walking = 1

Now,

As
`Time = (Distance )/(Speed)`

⇒ Time traveled by walking =
`(1)/(x)`

Now,

Given that - He runs twice as fast as he walks

⇒Speed of running = 2x

Also given distance traveled by running = 1

Time traveled by running =
`(1)/(2x)`

Now,

Given that - he cycles one and a half times as fast as he runs.

⇒Speed of cycling =
`(3)/(2)` (2x) = 3x

Also given distance traveled by cycling = 1

Time traveled by cycling =
`(1)/(3x)`

Now,

Total time traveled = Time traveled by walking + running + cycling

=
`(1)/(x)` +
`(1)/(2x)` +
`(1)/(3x)`

=
`(6+3+2)/(6x) = (11)/(6x)`

If he cycled the three mile , then total time taken =
`(1)/(3x)` +
`(1)/(3x)` +
`(1)/(3x)` = x

Given,

He takes ten minutes longer than he would do if he cycled the three miles

⇒x + 10 =
`(11)/(6) x`

⇒
`x - (11)/(6) x = -10`

⇒
`-(5)/(6)x = -10`

⇒x =
`(60)/(5)` = 12

⇒x = 12

∴ we get

Total time traveled by walking + running + cycling =
`(11)/(6) x = (11)/(6) (12) = 11 (2) = 22` min