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Q.

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.

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answer is 1.8.

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Detailed Solution

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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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.