A boat running upstream takes 8 hours 48 minu | vedclass

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Question

(C) Let the speed of the boat in still water be $u$ $km/h$ and the speed of the current be $v$ $km/h$.The time taken to cover a distance $D$ upstream

Vedclass · Accepted Answer

$8:3$

Vedclass · Answer

(C) Let the speed of the boat in still water be $u$ $km/h$ and the speed of the current be $v$ $km/h$.The time taken to cover a distance $D$ upstream is $8$ $hours$ $48$ $minutes = 8 + \frac{48}{60} = 8 + 0.8 = 8.8$ $hours$.Upstream speed $= u - v = \frac{D}{8.8} \implies D = 8.8(u - v)$.The time taken to cover the same distance $D$ downstream is $4$ $hours$.Downstream speed $= u + v = \frac{D}{4} \implies D = 4(u + v)$.Equating the two expressions for $D$:$8.8(u - v) = 4(u + v)$$2.2(u - v) = u + v$$2.2u - 2.2v = u + v$$1.2u = 3.2v$$\frac{u}{v} = \frac{3.2}{1.2} = \frac{32}{12} = \frac{8}{3}$.Thus,the ratio of the speed of the boat to the speed of the current is $8:3$.

$A$ boat running upstream takes $8$ $hours$ $48$ $minutes$ to cover a certain distance,while it takes $4$ $hours$ to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the current respectively?

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