P and Q are two points along the flow of a river. R is midpoint of line joining P and Q. Between P and R, speed of river is 2 km/hr. But j… — Answer & Discussion

P and Q are two points along the flow of a river. R is midpoint of line joining P and Q. Between P and R, speed of river is 2 km/hr. But just after R, speed of river becomes 4 km/hr till Q. The water is flowing from P to Q. The speed of boat in still water is 14 km/hr. If the boat takes 8 hours to cover distance P and Q, then find the distance between P and Q.

A112.67 km
B120 km
C135.63 km
D145.21 km

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Discussion 1

CCommunity06 Jul 2019

Let the distance between P and Q be T km.

Since river flows from P to Q, going from P to Q means going downstream.

Downstream speed between P and R = (14 + 2) km/hr = 16 km/hr

Downstream speed between R and Q = (14 + 4) km/hr = 18 km/hr

Since R is midpoint of P and Q, distance from P to R will be T/2 km and between R and Q will be T/2 km.

Time taken to go from P to Q = (T/2)/16 + (T/2)/18 = 8

⇒ T/32 + T/36 = 8

⇒ 17T/288 = 8

⇒ T = 2304/17 = 135.53

∴ Distance between P and Q is 135.63 km.