Question 184155

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

Let s=speed of the wind
With the wind, add wind speed; against the wind subtract
Time travelling with the wind= 240/(420+s)
Time travelling against the wind=240/(420-s)
Now we are told that the above two times add up to 1 hr 10min=1 1/6=7/6 hr so:
240/(420+s) +240/(420-s)=7/6  multiply each term by 6(420+s)(420-s)
1440(420-s)+1440(420+s)=7(420+s)(420-s) get rid of parens
1440*420-1440s+1440*420+1440s=7*176400-7s^2
YOU KNOW, THERE MAY BE AN EASIER WAY BUT THE ONLY THING I CAN SEE TO DO RIGHT NOW IS GRIND OUT THE BIG NUMBERS.

604800+604800=1234800-7s^2 this equals
1209600=1234800-7s^2 subtract 1234800 from each side
-7s^2=-25200 divide each side by -7
s^2=3600   take square root of each side
s=+or- 60 mph-------------------------------------------------speed of the wind
disregard the negative value for s; wind speed is positive

CK
240/(420+60) +240/(420-60)=7/6
240/480 + 240/360=7/6
1/2 + 2/3=7/6
3/6+ 4/6=7/6
7/6=7/6

Hope this helps---ptaylor