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 answers 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 jogging 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

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) ___________


`t = \frac 5 r`

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


`r + 1`

c. Write an expression for the time t(in hours) it takes to jog 5 miles
back to the park. ___________


`t =\frac 5 {r+1}`

d. Use your answers 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.

`T =\frac 5 {r} +\frac 5 {r+1} = ((5r+5)+5r)/(r(r+1))=(10r+5)/(r(r+1))`

e. Find the total jogging 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.


`T = (10r+5)/(r(r+1)) = (10(4)+5)/(4(4+1))=\frac 9 4 = 2.25` hours or 135 minutes

2.3 hours rounded I suppose.