SOLUTION: 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 th

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

RELATED QUESTIONS
an airplane can travel at 1000 miles with the wind in the same time it could travel with... (answered by lwsshak3)

A plane can travel 640 miles against the wind in the same time it can travel 800 miles... (answered by checkley77)

A plane can travel 640 miles against the wind in the same time it can travel 800 miles... (answered by nerdybill)

a plane can travel 480 mph in calm air. flying with the wind, the plane can travel 600... (answered by w_parminder)

A plane can fly 300 miles with the wind in the same amount of time as it can travel 210... (answered by josgarithmetic)

a plane traveling with the wind can travel 1170 miles in 3 hours. Against the same wind... (answered by TimothyLamb,Alan3354,Danielshinmath)

A small airplane can travel 210 mph in still air. The plane can fly 520 miles with the... (answered by greenestamps,mananth)

a plane takes 3 hours to travel 1,503 miles with the wind. It can travel only 1,179 miles (answered by ankor@dixie-net.com)

A plane flies 460 mph in calm air. Flying with the wind, the plane can travel 1560 miles... (answered by macston)