Question: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. 

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

Question:A man rows downstream 27 km and upstream 18 km, taking 3 hours each time. What is the velocity of the current ? 

Rate downstream` = (27/3)` km/hr

                            = 9 km/hr

Rate upstream` = (18/3)` km/hr

                        = 6 km/hr

:. Velocity of current` = 1/2 (9 - 6)` km/hr

                                = 1.5 km/hr

Question:A man can row 12 kmph in still water. If takes him twice as long to row up as to row down the river. Find the rate of stream. 

Let man's rate upstream be x kmph.

Then, his rate still water` = 1/2 (2x + x)` kmph` = (3x)/2` kmph

           `:. (3x)/2 = 12 or x = 8`

`:. (300)/(10 + x) = 8 or 300`

`= 80 + 8x or x`

`= (220)/8`

`= 55/2` m/sec.

:.  Speed of second train

`= (55/2 xx 18/5)` kmph

   = 99 kmph

Question:A man can row 8 kmph in still water and the river is running at 2 kmph. If the man takes 1 hour to row to a place and back, how far is the place ? 

Man's rate downstream = (8 + 2) kmph = 10 kmph.

Man's rate upstream = (8 - 2) kmph = 6 kmpn

Let the required distance be x km

Then,` x/10 + x/6 = 1 <=> 3x + 5x = 30 <=> x`

        `= 3.75` km

Hence, the required distance is 3.75 km.

Question: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. 

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 or 11x^2 - 240x - 44 = 0`

`:. 11x^2 - 242x + 2x - 44 = 0`

`or 11x (x - 22) + 2 (x - 22) = 0`

`or (x - 22) (11x + 2) = 0 or x = 22`

:. Speed of motorboat in still water = 22 kmph.

Question:A man can row 40 km upstream and 55 km downstream in 13 hours. Also he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current. 

Let, rate upstream = x km/hr & rate downstream = y km/hr.

Then,` 40/x + 55/y = 13 .......(i)`

and ` 30/x + 44/y = 10 ..... (ii)`

or 40u + 55v = 13 .....(iii)

and 30u + 44v = 10 .... (iv)

where `u = 1/x` and `v = 1/y`

On solving (iii) and (iv) we get `: u = 1/5` and v = 1/11`

:. x = 5 and y = 11

:. Rate in still water` = 1/2 (11 + 5)` kmph = 8 kmph.

Rate of current` = 1/2 (11 - 5)` kmph = 3 kmph