Boats and Streams Solved Problems and Answers

1. In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.

Explanation: 

Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph; Speed upstream = (x - 2) kmph.
=> 6/x+2 + 6/x-2 = 33/60
=> 11x² - 240x - 44 = 0
=> 11x² - 242x + 2x - 44 = 0
=> (x - 22) (11x + 2) = 0 ? x = 22.
Hence, speed of motorboat in strill water = 22 kmph.

2. A man can row 18 kmph in still water. It takes him trice as long to row up as to row down the river. Find the rate of stream.

Explanation: 

Let man’s rate upsream be x kmph. Then, his rate downstream = 3x kmph.
=> Rate in still water = 1/2(3x + x) kmph = 2x kmph.
So, 2x = 18 or x = 9.
=> Rate upstream = 9 km/hr, Rate downstream = 27 km/hr.
Hence, rate of stream = 1/2(27 - 9) km/hr = 9 km/hr.

3. A man can row upstream at 7 kmph and downstream at 10 kmph. Find man’s rate in still water and the rate of current.

Explanation: 

Rate in still water = 1/2 (10 + 7) km/hr = 8.5 km/hr,
Rate of current = 1/2 (10 - 7) km/hr = 1.5 km/hr.

4. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is :

Explanation:  

Rate upstream = (7/42)*60 kmh = 10 kmph. Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x-3 = 10 or x = 13 kmph.

5.  If a man can swim downstream at 6 kmph and upstream at 2 kmph, his speed in still waters : 

Explanation:  

Speed in still water = (1/2) * (6 + 2) km/hr
                             = 4 km/hr