Question

A cyclist travels 20 miles in the same amount of time it takes a hiker to walk 6 miles. The rate of the cyclist is 7 mph faster than the rate of the hiker. Find the rate Of the cyclist.

Answer 1

The speed of the cyclist is 10 miles per hour .

Explanation:

Given as :

The distance cover by cyclist =
`D_1`= 20 miles

The distance cover by biker =
`D_2` = 6 miles

The speed of biker =
`S_2` = s mph

The speed of cyclist =
`S_1`= 7 + s mph

The time taken by both cyclist and biker = t hour

Now. Distance = Speed × Time

So,
`D_1` =
`S_1` × t

Or, 20 = s × t

Or, t =
`(20)/(7+s)` .....1

And ,

`D_2` =
`S_2` × t

or, 6 = s t

Or, t =
`(6)/(s)` ....2

From Eq 1 and 2

I.e
`(20)/(7+s)` =
`(6)/(s)`

Or, 20 s = 6 ( 7 + s )

Or, 20 s - 6 s = 42

Or, 14 s = 42

∴ s =
`(42)/(14)`

I,e s = 3 miles per hour

So, The speed of biker =
`S_2` = s = 3 miles per hour

And The speed of cyclist =
`S_1`= 7 + s = 7 + 3= 10 miles per hour

Hence The speed of the cyclist is 10 miles per hour . Answer