Question 793207: Al was able to ride his bike 36mph with the wind, and 24 mph against the wind. The wind speed was 3mph. How fast does he ride with no wind?
Just looking at problem the answer should be 30. But when I try to use a formula I don't get 30.
t=d/r
36/x+3=24/x-3
36(x-3)=24(x+3)
36x-108=24x+72
12x=180
x=15
what am I doing wrong?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The problem does not make sense to me,
but what you are doing would be the solution to a different problem.
You were given his speeds with and against the wind.
You are also given the speed of the wind.
The speed of the wind should not really directly add to or subtract from the speed of a bike rider.
That works for a plane, which rides on the moving air, so the velocities are additive.
A bike rider pushes against the ground and is slowed by a headwind but by less than the speed of the headwind. A 10mph headwind slows a cyclist by 2-5 mph (depending on many factors). A tailwind may not increase the speed by the same amount.
If we assume the riding against the wind slows Al by  mph, and riding with the wind speeds him by mph, compared to his speed of  mph with no wind, then we have the system.
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It does not make sense that a 3 mph wind could do that, but the whole problem does not make sense.
Your equation and solution would be the right answer for a different problem.
If the problem stated that in the same time that he traveled a distance of 24 miles against the wind, he traveled 36 miles with the wind, and the wind velocity was additive,
 would be the time to travel 24 miles with a speed of  miles per hour, against the wind,
 miles per hour, with the wind,
and the equation  would make sense because the problem would have said that the times were the same.
AL would be riding 2 hours against the wind with a speed of 12 mph to travel 24 miles, and he would be riding with a speed of 18 mph with the wind for 2 hours covering 36 miles.
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