math word problem

Question

Against the wind a small plane flew 715 miles in 2 hours and 10 minutes. The return trip took only 1 hour nbspand 50 minutes. What was the speed of the​ wind? What was the speed of the plane in still​ air?

Answer 1

Let the speed of the plane be p and the speed of the wind be w.

The speed of the plane with the wind is p + w; the speed against the wind is p -w

1 hour 50 min = 110 min.

2 hr 10 min = 130 min

distance travelled is 715 miles

rt = d

Thus,

(p+w) 110 = 715

(p-w) 130 = 715

Expanding,

110 p + 110 w = 715

130 p - 130 w = 715

Multiply the bottom equation by 11/13

110 p - 110 w = 715 * 11/13

Subtract the bottom equation from the top equation

220w = 715 * 2/13

w = 715 * 2/13/220

w = 5 * 11 * 13 * 2/13/(2*2*5*11) = 1/2

130 p = 715 + 130 w

130 p = 715 + 130 * 1/2

130 p = 780

p = 6

p = 6 miles/min = 360 mph

w = 1/2 mile/min = 30 mph