Edward C. answered • 03/02/15

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The boy swims north at 4 m/s while being pushed east at 3 m/s. It will take him 50 s to cross the 200 m river. During this time he will have been pushed downstream 150 m. It will take him 20 s to run the 150 m at 7.5 m/s. So his total time will be 50 + 20 = 70 s.

The girl swims at an angle upstream such that the vector sum of her velocity at 4 m/s and the current at 3 m/s east will result in a vector heading due north. If you draw these vectors you will see they form a right triangle with the hypotenuse being her swim direction at 4 m/s, one leg being the current east at 3 m/s, and the other leg being her net velocity north. Her net velocity north is sqrt(4^2 - 3^2) = sqrt(7) m/s. It will take her 200/sqrt(7) = 75.593 s to swim across the 200 m river.

So the boy will win the race by 5.593 s