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