Question

A cyclist traveled 15 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 12 kilometers, the skater had gone 6 kilometers. Find the speed of the skater.

Answer 1

The speed of the skater is 15 kilometers per hour.

Explanation:

Let x be the rate of the skater.

Then the rate of the cyclist is x+15.

Let t represents time, so we get two equations:

(x+15)t = 12 and xt = 6

Now, solving for t;

`t=(12)/(x+15)` and
`t=(6)/(x)`

As t is the same for the skater and the cyclist, we will equate both the equations now.

`(12)/(x+15)=(6)/(x)`

Solving for x;

`12x=6(x+15)`

=>
`12x=6x+90`

=>
`12x-6x=90`

=>
`6x=90`

x = 15

Hence, the speed of the skater is 15 kilometers per hour.