Question

Two cyclists start at the same point and travel in opposite directions. One cyclist travels 10 mih slower than the other. If the two cyclists are 104 miles apart after 4 hours, what is the rate of each cyclist?

Answer 1

The speed of slower cyclist is 8 miles per hour

The speed of faster cyclist is 18 miles per hour

Solution:

One cyclist travels 10 min slower than the other

Let "x" be the speed of slower cyclist

Then, x + 10 is the speed of faster cyclist

The distance is given by formula:

`distance = speed * timetaken`

Distance of slower cyclist =
`x * 4`

Distance of slower cyclist = 4x

Distance of faster cyclist =
`(x + 10) * 4 = 4x + 40`

The two cyclists are 104 miles apart after 4 hours

4x + 4x + 40 = 104

8x + 40 = 104

8x = 104 - 40

8x = 64

x = 8

Thus rate of each cyclist is:

speed of slower cyclist = x = 8 miles per hour

speed of faster cyclist = x + 10 = 8 + 10 = 18 miles per hour