Two cyclists leave towns 180 kilometers apart at the same time and travel toward each other. One cyclist travels 4 km/h slower than the other. If they meet in 5 hours, what is the rate of each cyclist?

Answer :

We have the next formula

[tex]\text{distance}=\text{rate}\times\text{ time}[/tex]

In this case x is the faster speed and x-4 is the slower speed, we have the next equation

[tex]180=5x+5(x-4)[/tex]

We simplify

[tex]180=5x+5x-20[/tex][tex]180=10x-20[/tex]

Then we need to isolate the x

[tex]10x=200[/tex][tex]x=\frac{200}{10}=20[/tex]

Then for x-4

20-4=16

The rates of the cyclists are

16 km/hr

20 km/hr