SOLUTION: Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip. a. Find the bi

Question 269393: Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike takes 3 hours. The wind speed remains constant during the trip.
a. Find the bicyclist's average speed for each leg of the trip.
b. Write a system of linear equations that represent the situation.
c. What is the bicyclist's average speed in still air? What is the speed of the wind?
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = wind speed
Let = bike's speed with no wind
The trip that takes less time is with the wind
The 2 equations to use are:
(against the wind)
(with the wind)
given:

hrs
hrs
-------------------
The only unknowns are and ,
so I've got 2 equations and 2 unknowns
(1)
(1)
(1)
and
(2)
(2)
(2)
------------------------
Add the equations
(2)
(1)

and, since

------------
(a)
The bicyclist's average speed for the 1st leg:

mi/hr
The bicyclist's average speed for the 2nd leg:

mi/hr
----------------------
(b)

and

-----------------------
(c)
In still air the cyclist's speed is mi/hr
The wind seed is mi/hr

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What connection is there between wind speed and bicycle speed?
It's not possible to calculate wind speed from this info.

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