Question

You have jogged 5 miles from the park at a rate of r miles per hour. on your way back to the park your average speed increases by 1 mile per hour
a) write an expression for the time t(in hours ) it takes to jog 5 miles from the park as a function of your average speed r ( in miles per hour )

b) when you run back to the park, your average speed increases by 1 mph. Write an expression representing your new speed.

c) Write an expression for the time t(in hours ) it takes to jog 5 miles back to the park
d) use your answer to parts 'a' and 'c' to write an expression that gives the total jogging time T (in hours) as a function of your average speed r(in miles per hour ) when you are jogging away from the park. Write your answer as a single rational expression.
e) Find the total time if you jogged away from the park at an average speed (r) of 4 miles per hour. Round your answer to the nearest tenth

Answer 1

1. If you have jogged 5 miles from the park at a rate of r miles per hour, then the time you need to do this is $\frac{5}{r}$ hours ($S=v\cdot t$, where S is distance, v-speed and t-time).

2. When you run back to the park, your average speed increases by 1 mph and become r+1 mph.

3. It takes $\frac{5}{r+1}$ hours to jog 5 miles back to the park

4. The total jogging time T is $\frac{5}{r} + \frac{5}{r+1}$ hours.

5. If you jogged away from the park at an average speed of 4 miles per hour, then r+1=4 and r=3. The expression $\frac{5}{r} + \frac{5}{r+1}$will take look 
$\frac{5}{3} + \frac{5}{4}=\frac{5\cdot4+5\cdot 3}{12} =\frac{35}{12}=2.9$hours.