SOLUTION: This question(200898) is in your data base but i am not positive if it is correct. I was told there is a answer. Could somebody else PLEASE look at this problem again and work it t

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Question 200936: This question(200898) is in your data base but i am not positive if it is correct. I was told there is a answer. Could somebody else PLEASE look at this problem again and work it to verify if it is correct or wrong. I would really appreciate it..Thanks
Question:
A biker can travel 18 mph with no wind. The same rider can bicycle 8 mi against the wind in the same time it takes to bicycle 12 miles with the wind. What is the speed of the wind?

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = speed of the wind (in mph)


First, let's set up the equation involving the trip against the wind:


d=rt Start with the distance-rate-time formula


8=%2818-w%29t Plug in d=8 and r=18-w (the wind slows him down, so you must subtract "w" from 18)


8%2F%2818-w%29=t Divide both sides by 18-w.


t=8%2F%2818-w%29 Rearrange the equation


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d=rt Go back to the distance-rate-time formula


12=%2818%2Bw%29t Plug in d=12 and r=18%2Bw (the wind speeds him up, so you must add "w" to 18)


12%2F%2818%2Bw%29=t Divide both sides by 18%2Bw.


t=12%2F%2818%2Bw%29 Rearrange the equation

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Now recall that he "can bicycle 8 mi against the wind in the same time it takes to bicycle 12 miles with the wind". So this means that the times "t" are the same variable. This means that we can plug one equation into another:


t=12%2F%2818%2Bw%29 Start with the given equation.


8%2F%2818-w%29=12%2F%2818%2Bw%29 Plug in t=8%2F%2818-w%29


8%2818%2Bw%29=12%2818-w%29 Cross multiply


144%2B8w=216-12w Distribute.


8w=216-12w-144 Subtract 144 from both sides.


8w%2B12w=216-144 Add 12w to both sides.


20w=216-144 Combine like terms on the left side.


20w=72 Combine like terms on the right side.


w=%2872%29%2F%2820%29 Divide both sides by 20 to isolate w.


w=18%2F5 Reduce.


w=3.6 Divide (either use a calculator or long division)


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Answer:

So the solution is w=3.6 which means that the speed of the wind is 3.6 mph.


Note: if you are expecting a whole number for an answer, I would verify that you have the correct problem written down.