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. 

Sol. 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/x2 = 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. 

Sol. 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. 

Sol. 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.
