PLEASE HELP!!! I WILL 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
