Q36 of 27 Page 1

A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.

Let speed of the boat in still water =x km/hr, and


Speed of the current =y km/hr


Downstream speed = (x + y) km/hr


Upstream speed = (x − y) km/hr


… (1)


… (2)


Let


Put in the above equation we get,


24u + 16v = 6


Or, 12u + 8v = 3 ... (3)


36u + 12v = 6


Or, 6u + 2v = 1 ... (4)


Multiplying (4) by 4, we get,


24u + 8v = 4v … (5)


Subtracting (3) by (5), we get,


12u = 1


⇒u = 1/12


Putting the value of u in (4), we get, v = 1/4


⇒ = 1/12 and = 1/4


⇒x + y = 12 and x – y = 4


Thus, speed of the boat in still water = 8 km/hr,


Speed of the current = 4 km/hr


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