A plane can fly 230 miles downwind in the same amount of time as it can travel 180 miles upwind.Find the velocity of the wind of the plane can fly 250 mph in still air

Answer 1

230 = (r+s)* t = rt + st

180 = (r-s)*t = rt - st

50 = 2st

25 = st

So then rt = 205

t = 205/r = 25/s

205s = 25r

205s/25 = r

(41/5)s = r

180 = [(41/5)s - s ] * t

180 = (36/5)s * t

180 * 5/ 36 = t

900/36 = t

t = 25

230 = [(41/5)s + s ]* t

230 = (46/5)s * t

230/t = (46/5)s

230/25 = (46/5)s

230/25* 5/46 = s

230/5 * 1/46 = s

230/230 = s

s = 1

180 = rt - st

180 = rt - t since s=1

180 = t ( r-1)

180 = 25(r-1)

180/25 = r-1

36/5 = r - 1

41/5 = r

8 and 1/5 = r

8.2 = r

250/8.2 = 30.487804