SOLUTION: A plane can fly 190 mph in calm air. Flying with the wind, the plane can fly 836 mi in the same amount of time it takes to fly 684 mi against the wind. Find the rate of the wind.

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Question 1177801: A plane can fly 190 mph in calm air. Flying with the wind, the plane can fly 836 mi in the same amount of time it takes to fly 684 mi against the wind. Find the rate of the wind.

Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!
t = d/r times equal:

836(190-w) = 684(190+w)
152*190 = 684w + 836w
152*190/ 1520 = w
19mph = w

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
rate * time = distance.

rate of the plane = r = 190 mph
rate of the wind = w
distance = d = 836 with the wind and 684 against the wind.
t = the time

with the wind, the formula becomes (190 + w) * t = 836.
against the wind, the formula becomes (190 - w) * t = 684.

the rate of the wind and the rate of the plane and the time in both equations is the same.

simplify both equations to get:

190 * t + w * t = 836
190 * t - w * t = 684

add both equations together to get 380 * t = 1520

solve for t to get t = 1520 / 380 = 4

replace t in the first equation with 4 to get 190 * 4 + w * 4 = 836

simplify to get 760 + 4w = 836

subtract 760 from both sides of the equation to get 4w = 76

solve for w to get w = 19

that should be your answer.

replace t with 4 and w with 19 in both original equationt to conffirm the solution is correct.

190 * 4 + 19 * 4 = 836 becomes 836 = 836, confirming this equation is good.
190 * 4 - 19 * 4 = 684 becomes 684 = 684, confirming this equation is good.

the solution is confirmed to be good.

the solution is the rate of the wind is 19 miles per hour.