Two men, A and B, start at the same point, walk in opposite directions, and reach their respective destinations, X and Y, each in one hour. Had they exchanged destinations from the start, A would have arrived at Y 35 minutes after B would have arrived at X. Find the ratio of A's speed to B's speed.
+128731 A must walk at a rate of X mph
B must walk at at a rate of Y mph
And when they switch destinations
Y / X = X / Y + 35/60
Y / X = X /Y + 7/12
Y/X - X/Y = 7/12
Y^2 - X^2 7
_________ = ____
XY 12
12 (Y^2 - X^2) = 7XY
12Y^2 - 12X^2 = 7XY
12Y^2 - 7XY - 12X^2 = 0
(4Y + 3X) (3Y - 4X) = 0
Only the second factor gives us what we want
3Y - 4x = 0
4X = 3Y
X = (3/4)Y
X/Y = 3/4
So.....the ratio of A's speed to B's speed must be X : Y = 3 : 4
