On a river,Q is the midpoint between two poin | vedclass

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(D) Let the speed of the boat in still water be $u$ km/h and the speed of the stream be $v$ km/h. Let the distance between $P$ and $Q$ be $d$ km. Then

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$7 \frac{1}{3}$

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(D) Let the speed of the boat in still water be $u$ km/h and the speed of the stream be $v$ km/h. Let the distance between $P$ and $Q$ be $d$ km. Then $PQ = QR = d$ km and $PR = 2d$ km.The time taken to travel from $P$ to $Q$ and back is given by:$\frac{d}{u-v} + \frac{d}{u+v} = 12$ hours  ---$(1)$The time taken to travel from $P$ to $R$ (downstream) is:$\frac{2d}{u+v} = 16 	ext{ hours } 40 	ext{ minutes} = 16 + \frac{40}{60} = 16 + \frac{2}{3} = \frac{50}{3}$ hours  ---$(2)$From $(2)$,we get $\frac{d}{u+v} = \frac{25}{3}$ hours.Substitute this into $(1)$:$\frac{d}{u-v} + \frac{25}{3} = 12$$\frac{d}{u-v} = 12 - \frac{25}{3} = \frac{36-25}{3} = \frac{11}{3}$ hours.We need to find the time taken to travel from $R$ to $P$ (upstream),which is $\frac{2d}{u-v}$:$\frac{2d}{u-v} = 2 	imes \frac{11}{3} = \frac{22}{3} = 7 \frac{1}{3}$ hours.

On a river,$Q$ is the midpoint between two points $P$ and $R$ on the same bank. $A$ boat can travel from $P$ to $Q$ and back in $12$ hours,and from $P$ to $R$ in $16$ hours $40$ minutes. How long would it take to travel from $R$ to $P$? (in hours)

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