Quants 22 - Boats and Streams

Key Points to Remember:

In water, the direction along the stream is called downstream. The direction against the stream is called upstream. 

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then,

Speed downstream = u+v km/hr

Speed upstream = u-v km/hr

If the speed downstream is a km/hr and the speed upstream is b km/hr, then,

Speed in still water = 1/2 (a+b) km/hr

Rate of stream = 1/2 (a-b) km/hr

Practice Questions:

Question 1:

In 1 hour, a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in km/hr is,

Speed in still water = 1/2 ( 11 + 5 ) = 1/2(8) = 4 kmph

Question 2:

A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is, 

Speed of stream = 1/2 ( 13 - 8 ) = 1/2 (5) = 2.5 kmph

Question 3:

A man rows downstream 32 kmph and 14 kmph upstream. If he takes 6 hours to cover each distance, then the velocity in kmph of the current is,

Rate downstream = 32/6 kmph
Rate upstream = 14/6 kmph
Velocity of current = 1/2 (32/6 - 14/6) = 1/2 (18/6) = 1/2 (3) = 1.5 kmph

Question 4:

A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

Rate downstream = 16/2 = 8 kmph
Rate upstream = 16/4 = 4 kmph
Speed in still water = 1/2 (8 + 4) = 1/2 (12) = 6 kmph

Question 5:

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

Rate downstream = 1/10 * 60 = 6 kmph
Rate upstream = 2 kmph
Speed in still water = 1/2 ( 6 + 2 ) = 1/2 (8) = 4 kmph
Required time = 5 / 4 = 1 (1/4) = 1 hr 15 min. 

Time to Think:

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.