Two boats, A and B, move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines, the boat A along the river, and the boat B across the river. Having moved off an equal distance from the buoy the boats returned. Find the ratio of times of motion of boats $$tA/tB$$ if the velocity of each boat with respect to water is $$1.2$$ times greater than the stream velocity.

Question

Infinity Learn · Accepted Answer

Time taken to move in downstream direction, tdownstream $$=lv+uTime$$ taken to move in upstream direction, tupstream $$=lv$$−uTotal time taken for boat A, $$tA=lv+u+lv$$−$$u=2vlv2$$−$$u2=2(v/u)luv2/u2$$−$$1Time$$ of motion of boat B, $$tB=lv2$$−$$u2+lv2$$−$$u2=2lv2$$−$$u2$$                                             $$=2luv2/u2$$−$$1tAtB=2(v/u)luv2/u2$$−$$1$$×$$uv2/u2$$−$$12l$$                                               $$=(v/u)v2/u2$$−$$1=1.2(1.2)2$$−$$1=1.8$$

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