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

Answer:

The speed of the cyclist is 10 miles per hour .

Step-by-step 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 = $\frac{20}{7+s}$             .....1

And ,

$D_2$ =   $S_2$ × t

or, 6 = s t              

Or,  t = $\frac{6}{s}$  ....2

From Eq  1 and 2

I.e $\frac{20}{7+s}$ = $\frac{6}{s}$

Or, 20 s = 6 ( 7 + s )

Or, 20 s - 6 s = 42

Or, 14 s = 42

∴   s = $\frac{42}{14}$

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