SOLUTION: a cyclist travels 5 miles each way on a bike path travel in one direction is with a 4 mile per hour wind and travel back against a 4 mile per hour wind a. write and simplify a

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Question 826462: a cyclist travels 5 miles each way on a bike path travel in one direction is with a 4 mile per hour wind and travel back against a 4 mile per hour wind
a. write and simplify an equation for the amount of time t hours it will take the cyclist to make the trip.

b. what is the cyclist total travel an average of 6 miles per hour without the wind.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Can we do #a without using any of #b ?

r = speed when no wind
c = speed of the wind; c=4


One Direction___________r+4___________t_______________5
OtherDirection__________r-4___________(5/(r-4))_______5
Total Time__________________________t+5/(r-4)

What we also can find is:
One Direction___________r+4___________5/(r+4)_______________5
OtherDirection__________r-4___________(5/(r-4))_______5
Total Time__________________________highlight%285%2F%28r%2B4%29%2B5%2F%28r-4%29%29

Simplifying the total time:
%285%28r-4%29%2B5%28r%2B4%29%29%2F%28r%5E2-16%29
%285r-20%2B5r%2B20%29%2F%28r%5E2-16%29
highlight%28%2810r%29%2F%28r%5E2-16%29%29

I will leave #b undone here, but if you cannot solve it yourself and still want help, just ask.