SOLUTION: Please help! I'm not sure how to set this problem up to solve. Jeanie bicycles 33 km/h with no wind. Against the wind she bikes 75 km in the same time it takes to bike 123 km wi

Question 47900: Please help! I'm not sure how to set this problem up to solve.
Jeanie bicycles 33 km/h with no wind. Against the wind she bikes 75 km in the same time it takes to bike 123 km with the wind. What is the speed of the wind?
Thanks!
Answer by pizza(14) (Show Source): You can put this solution on YOUR website!
Right then, this is better done with algebra, which is no doubt why you posed the question here.

Let the speed of the wind be w.
Then Jeanie's speed with the wind is 33+w.
And Jeanies's speed against the wind is 33-w.

Then, the time Jeanie bikes 75km against the wind is 75/(33-w)
And also, the time Jeanie bikes 123km with the wind is 123/(33+w)
which, as the question says, is the same.
Therefore,
75/(33-w) = 123/(33+w)
which becomes, after cross multiplying

which becomes

which means w = 1584/198 = 8
And thus, putting back the units, we have the speed of the wind is 8 km/h

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