<PRE><B>Question 1177801</B>
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.





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