Question 83704
Let r=rate of wind

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

time it takes to run 10 mi with the wind:
t=10/(5+r)

time it take to run 7 mi against the wind:

t=7/(5-r) 

Now we are told that these two times are the same, so:

10/(5+r)=7/(5-r)  multiply both sides by(5+r)(5-r) to get rid of fractions. In other words, cross multiply:

10(5-r)=7(5+r)  get rid of parens

50-10r=35+7r subtract 7r and also 50 from both sides

50-50-10r-7r=35-50+7r-7r  collect like terms

-17r=-15 divide both sides by -17

r=0.882 mph-------------------------------------------rate of wind

ck

10/(5+0.882)=7/(5-0.882)

10/5.882=7/4.118

~1.7=~1.7

Hope this helps-----ptaylor