1. ## Speed of Wind

A girl ran 41 miles with the wind at her back and then ran 39 miles in the same amount of time with the wind against her. if her pace without any wind is 8 miles/hr, how fast is the wind?

2. Originally Posted by sharkman
A girl ran 41 miles with the wind at her back and then ran 39 miles in the same amount of time with the wind against her. if her pace without any wind is 8 miles/hr, how fast is the wind?
Hi sharkman,

If we believe that the wind will aid a runner the same way that a current would aid a boat, then

Let w = rate of wind

Let w + 8 = rate of girl with the wind (traveling 41 miles)

Let w - 8 = rate of girl against the wind (traveling 39 miles)

D = rt

Since t is constant, t = D/r

$\frac{41}{8+w}=\frac{39}{8-w}$

3. ## Thanks

Originally Posted by masters
Hi sharkman,

If we believe that the wind will aid a runner the same way that a current would aid a boat, then

Let w = rate of wind

Let w + 8 = rate of girl with the wind (traveling 41 miles)

Let w - 8 = rate of girl against the wind (traveling 39 miles)

D = rt

Since t is constant, t = D/r

$\frac{41}{8+w}=\frac{39}{8-w}$
Thank you for the equation set up.
If I could somehow learn the skill of converting word problems to proper equations, I would fall in love all over again.

4. But, of course, the wind does NOT "aid a runner the same way that a current would aid a boat" (or as wind aids an airplane). The wind blows against a runner setting up a slight amount of resistance. The boat floats on the current so the current is added to its motion through the water- imagine a toy car running on table while the table is carried to one side.

In my opinion, this is a completely mistaken problem.

5. ## ok

Originally Posted by HallsofIvy
But, of course, the wind does NOT "aid a runner the same way that a current would aid a boat" (or as wind aids an airplane). The wind blows against a runner setting up a slight amount of resistance. The boat floats on the current so the current is added to its motion through the water- imagine a toy car running on table while the table is carried to one side.

In my opinion, this is a completely mistaken problem.
I got 1/80 mph for the speed of wind.

6. Originally Posted by sharkman
I got 1/80 mph for the speed of wind.
Work through that again. You have made a mistake in your algebra somewhere.

$41(8-w)=39(8+w)$