Solve the problem.
-A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?
A) Bike: $13 \mathrm{mph}$
Hike: $3 \mathrm{mph}$
B) Bike: $12 \mathrm{mph}$
Hike: $2 \mathrm{mph}$
C) Bike: $11.5 \mathrm{mph}$
Hike: $1.5 \mathrm{mph}$
D) Bike: $14.5 \mathrm{mph}$
Hike: $4.5 \mathrm{mph}$

Question

Quizplus · Accepted Answer

Let the hiking rate be $ x $ mph. Then the biking rate is $ x + 10 $ mph. The time for biking is $ \frac{12}{x+10} $ hours and for hiking is $ \frac{8}{x} $ hours. The equation is $ \frac{12}{x+10} + \frac{8}{x} = 5 $. Solving gives $ x = 2 $ mph for hiking and $ x + 10 = 12 $ mph for biking.

Solve the Problem 13mph13 \mathrm{mph}13mph Hike 3mph3 \mathrm{mph}3mph B) Bike 12mph12 \mathrm{mph}12mph Hike 2mph2 \mathrm{mph}2mph

Solve the Problem $13 \mathrm{mph}$ Hike $3 \mathrm{mph}$ B) Bike $12 \mathrm{mph}$ Hike $2 \mathrm{mph}$