Question 159526: A plane traveling against a wind can travel at 500 miles in the same time it can travel 1120 miles with the same wind. If the speed of the plane with no wind is 240 mph, what is the speed of the wind?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed (rate) of the wind
(Note: we must add the speed of the wind when travelling with the wind and subtract when we are travelling against the wind)
time travelling against the wind=500/(240-r)
time travelling with the wind=1120/(240+r)
Now we are told that the above two times are equal, so our equation to solve is:
500/(240-r)=1120/(240+r) multiply each side by (240-r)(240+r) or cross-multiply
500(240+r)=1120(240-r) get rid of parens
120000+500r=268800-1120r divide each term by 20 (just to reduce the side of the numbers)
6000+25r=13,440-56r add 56r and subtract 6000 from each side
6000-6000+25r+56r=13,440-6000-56r+56r collect like terms
81r=7440 divide each side by 81
r=91.852 mph-------------------------------speed of wind
CK
500/(240-91.852)=1120/(240+91.852)
3.375=3.375
Hope this helps---ptaylor
|
|
|
