Answer
$12$ miles per hour.
Work Step by Step
Let the walking rate be $x$.
Cycling rate was $3$ times faster than the walking rate.
Cycling rate $=3x$.
Formula for the time is $=\frac{Distance}{Speed}$.
Time taken to ride $60$ miles $=\frac{60}{3x}$.
Time taken to ride $8$ miles $=\frac{8}{x}$.
The total time spent cycling and walking was $7$ hours.
$\Rightarrow \frac{60}{3x}+\frac{8}{x}=7$
Multiply both sides by $3x$ to clear fractions.
$\Rightarrow 3x\left (\frac{60}{3x}+\frac{8}{x}\right )=(3x)(7)$
Use distributive property.
$\Rightarrow 3x\left (\frac{60}{3x}\right )+3x\left (\frac{8}{x}\right )=21x$
Cancel common terms.
$\Rightarrow 60+24=21x$
Add like terms.
$\Rightarrow 84=21x$
Divide both sides by $21$.
$\Rightarrow \frac{84}{21}=\frac{21x}{21}$
Simplify.
$\Rightarrow 4=x$
Cycling rate $3x=3(4)=12$ miles per hour.
