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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 7-8, Math Kangaroo 9-10.
As Harvey rowed on, Long Jack slipped and fell overboard. In the ice cold water, he treaded water while a current was pulling him away from Harvey's boat at a speed of 0.5 mph. Harvey noticed Long Jack's absence after only 2 minutes and started rowing back at double his usual speed. How many minutes did Long Jack spend in the water in total?
(characters from Rudyard Kipling's "Captains Courageous").
First, we have to notice that the speed of the current can be ignored since it is constant and affects all the moving objects in the same way. Therefore, we can assume it to be zero.
The problem is now reduced to Long Jack standing motionless while Harvey rows away from him for 2 minutes and back towards him for an unknown time x minutes. Since Harvey is able to double his speed on the way back, the time he will put to cover the same distance he covered on the way away from Long Jack, is only half of the previous time.
Therefore, Long Jack spent 3 minutes in the water.