Iwill give brainliest answer 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.

A. The expression for the time t it takes to jog 5 miles from the park as a function of r, we shall proceed as follows:
time=(distance)/speed
time=t
distance=5 miles
speed=(r) miles per hour
plugging the values in the formula we get:
t=5/(r) 

b.  When you run back to the park, your average speed increases by 1 mph. Write an expression representing your new speed.
Given that on the way back, the speed increases by 1 mph, the expression representing new speed will be:
initial speed=r mph
new speed=r+1=(r+1) mph

c.  Write an expression for the time t(in hours) it takes to jog 5 miles back to the park.
Here we shall use the formula:
Time taken for the jog 5 miles back to the park will be given by:
time=distance/speed
distance=5 miles
speed=(r+1) mph 
thus
time=5/(r+1) hours

d. The expression for total jogging time will be given by:
Total time=5/r+5/(1+r)
=[5(1+r)+5r]/[r(1+r)]
=[5+5r+5r]/[r(1+r)]
=(5+10r)/[r(1+r)]

e] The total time of jogging given that r=4 mph will be:
plugging r=4 in the answer from (d) we get:
(5+10r)/[r(1+r)]
=(5+10*4)/[4(1+4)]
=(5+40)/(4(5))
=45/20
=2.25 hours

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