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Two persons P and Q crosses the river st...

Two persons P and Q crosses the river starting from point A on one side to exactly opposite point B on the other bank of the river. The person P crosses the river in the shortest path. The person Q crosses the river in shortest time and walks back to point B. Velocity of river is 3 kmph and speed of each boat is 5 kmph w.r.t river. If the two persons reach the point B in the same time, then the speed of walk of Q is

Text Solution

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`t_(P) = (d)/(sqrt(V_(B)^(2) - V_(W)^(2))) = (d)/(sqrt(5^(2) - 3^(2))) = (d)/(4)`
`t_(Q) = (d)/(V_(B)) = (d)/(5), t_(P) = t_(Q) + Delta t`
`(d)/(4) = (d)/(5) + (x)/(V_("man")), " "` But `x = V_(W) (d)/(V_(B))`
`(d)/(4) = (d)/(5) + (V_(W)d)/(V_(B)V_("man")), (cancel(d))/(4) = (cancel(d))/(5) + (3cancel(d))/((5)V_("man"))`
`(1)/(4) - (1)/(5) = (3)/(5V_("man")), (1)/(20) = (3)/(5V_("man"))`
`V_("man") = ((3)(20))/(5) = 12` kmph
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