Question

If Bill rides his bike 3 miles to Fred's house and then walks with Fred the remaining 1 mile to school, it will take him 30 min. But if he rides the entire distance, it will take him only 20 minutes. Find his biking speed and walking distance?

Answer 1

r * t = d, therefore t = d/r

Let x and y equal Bill's riding speed and walking speed in miles per hour respectively.

Then from the problem narrative,\[\left\{\frac{30}{60}\text{=}\frac{3}{x}+\frac{1}{y},\frac{20}{60}=\frac{4}{x}
\right\} \]Solve the simultaneous equations for x and y.\[\{x=12,y=4\} \]Bill's riding speed is 12 mph and walking speed is 4 mph.
The only "walking distance" in the problem was the one mile from Fred's house to school.