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.
1). 112.67 km
2). 120 km
3). 135.63 km
4). 145.21 km
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.10. A car goes 20 meters in a second. Find its speed in km/hr.