Travelling at full speed agaist the current of a river, a motorboat moves at the rate of 12 kilometers per hour relative to the land. Travelling at half speed with the current, it moves 8 kilometers per hour. find the maximum speed of the boat in still water.
Let x = maximum speed in still water in k/h Let y = speed of the river current in k/h. The river current slows the boat down from speed x k/h to x-y k/h, so >>...travelling at full speed agaist the current of a river, a motorboat moves at the rate of 12 kilometers per hour relative to the land...<< tells us x - y = 12 When the boat travels at half speed with the current, the current speeds up the boat from half speed (1/2)x k/h to (1/2)x+y k/h, so >>...travelling at half speed with the current, it moves 8 kilometers per hour...<< tells us (1/2)x + y = 8 so we have this system of 2 equations in 2 unknowns: x - y = 12 (1/2)x + y = 8 Can you solve that? x = 40/3 k/h, y = 4/3 k/h So the boat goes 13 1/3 k/h in still water, and the current\'s speed is 1 1/3 k/h
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