After [tex]h[/tex] hours, the distance the runner went is
[tex]4h[/tex]
and the distance the cyclist went is
[tex]19(h-3)[/tex]
Set the two equations equal and solve for [tex]h[/tex]:
[tex]4h=19(h-3)[/tex]
[tex]\Rightarrow 4h=19h-57[/tex]
[tex]\Rightarrow -15h=-57[/tex]
[tex]\Rightarrow h=\frac{57}{15}[/tex]
[tex]\Rightarrow h=\frac{19}{5}[/tex]
[tex]\Rightarrow h=3.8[/tex]
The cyclist traveled [tex]h-3[/tex] hours, which is 0.8 hours
