A man rows a certain distance downstream in X hours and returns the same distance in Y hours. If the stream flows at the rate of Z km/h, then the speed of the man in still water is given by
And if speed of man in still water is Z km/h then the speed of stream is given by
Example 5: Vikas can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the stream flows at the rate of 3 km/h, find the speed of Vikas in still water.
Solution: By the formula,
Vikas’s speed in still water
= 15 km/h
If a man capable of rowing at the speed u of m/sec in still water, rows the same distance up and down a stream flowing at a rate of v m/sec, then his average speed through the journey is
Example 6: Two ferries start at the same time from opposite sides of a river, travelling across the water on routes at right angles to the shores. Each boat travels at a constant speed though their speeds are different. They pass each other at a point 720 m from the nearer shore. Both boats remain at their sides for 10 minutes before starting back. On the return trip they meet at 400 m from the other shore. Find the width of the river.
Solution: Let the width of the river be x.
Let a, b be the speeds of the ferries.
(Time for ferry 1 to reach other shore + 10 minute wait + time to cover 400m) = Time for freely 2 to cover 720m to other shore + 10 minute wait + Time to cover (x – 400m) )