A man rode a bicycle for 12 miles and hiked an additional 8 miles. The total time for the trip was 5 hours. If his bicycling rate was 10 miles per hour faster than his hiking rate, then what was his hiking rate?
A) $2 \mathrm{mph}$
B) $4 \mathrm{mph}$
C) $1 \mathrm{mph}$
D) $3 \mathrm{mph}$

Question

Quizplus · Accepted Answer

Let the hiking rate be $x$ mph. Then the bicycling rate is $x+10$ mph.Time taken for bicycling = $\frac{12}{x+10}$ hoursTime taken for hiking = $\frac{8}{x}$ hoursTotal time = $\frac{12}{x+10}+\frac{8}{x}=5$$\Rightarrow \frac{12x+80+8x+100}{x(x+10)}=5$$\Rightarrow 20x+180=5x(x+10)$$\Rightarrow 20x+180=5x^2+50x$$\Rightarrow 5x^2+30x-180=0$$\Rightarrow x^2+6x-36=0$$\Rightarrow (x+12)(x-3)=0$$\Rightarrow x=-12,3$Since the rate cannot be negative, the hiking rate is $3$ mph.

A Man Rode a Bicycle for 12 Miles and Hiked 2mph2 \mathrm{mph}2mph

A Man Rode a Bicycle for 12 Miles and Hiked $2 \mathrm{mph}$