a plane traveling at a constant speeed goes 1200 miles with the wind. then turns around and travels to 1000 miles against the wind.

Question

a plane traveling at a constant speeed goes 1200 miles with the wind. then turns around and travels to 1000 miles against the wind. If the speed of the wind is 10 mph and the total flight took 5 hours, find the speed of the plane in still air

Answer 1

one way to narrow down the likely range for the solution is

to calculate an average speed. 1000+ 1200 miles = total 2200 miles in 5 hours, for an average speed of 2200/5 = 440 mph = a good estimate.

Let T = the time traveled with the wind, and P = plane's speed with no wind, Then T(P+10) = 1200

TP + 10T = 1200

5-T = time traveled against the wind

(5-T)(P-10) = 1000

5P -50 - TP + 10T = 1000

add two equations together

TP + 10T = 1200

-TP +10T +5P =1050

20T+5P = 2250

divide by 5

4T + P = 450

P = 450 -4T = plane's speed with no wind

since 0<T<5 hours

430<P<450 mph

P = 440

T(440+10) = 1200

T = 1200/450 = 2 2/3 hours with the wind

5-T = 2 1/3 hours against the wind

(2 1/3)(440-10) = 1003 1/3 miles which is close to 1000.