SOLUTION: a small plane cruises at 180 mph. it takes the same amount of time to travel 7 miles with the wind as it takes to travel 5 miles against the wind. what is the wind speed?

Question 271882: a small plane cruises at 180 mph. it takes the same amount of time to travel 7 miles with the wind as it takes to travel 5 miles against the wind. what is the wind speed?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
a small plane cruises at 180 mph. it takes the same amount of time to travel 7 miles with the wind as it takes to travel 5 miles against the wind. what is the wind speed?
Let w be the wind speed and t the time traveled. Then using distance = rate*time we have:
1.) 7 = (180+w)*t (with the wind)
2.) 5 = (180-w)*t (against the wind)
Expanding we have:
From 1.) we have t = 7/(180+w)
Substituting 7/(180+w) for t in 2.) we have:
5 = (180-w)*(7/(180+w))
Multiply both sides above by (180+w):
5*(180+w) = (180-w)*7
900+5w = 1260-7w
Solve the above for w.

RELATED QUESTIONS
a small plane can travel at 110 mph in calm air. flying with the wind, the plane can fly... (answered by DrBeeee)

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

a six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with... (answered by Paul)

A six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the (answered by ptaylor)

A 6 passenger plane cruises at 180 mph in calm air,if the plane flies 7 miles with the... (answered by richwmiller)

A six passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the (answered by solver91311,nyc_function)

A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with... (answered by Fombitz)

A six passenger plane cruises at 180 mph in calm air.If the plane flies 7 miles with the... (answered by jim_thompson5910)

A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with... (answered by mananth)