Question

A motorboat goes downstream and covers a distance in 4 hours while it covers the same distance upstream in 5 hours if the speed of the stream is 3 km per hour find speed of motor boat in still water

Answer 1

Let x km/hr and y km/hr be the speed of the motorboat in still water and the speed of the stream respectively.
Then,
Speed of boat going downstream = (x-y)km/hr
= (x-3) km/hr
Distance travelled downstream = (x-3)/4 km
And,
Speed of boat going upstream = (x+y) km/hr
= (x+3)km/hr
Distance travelled upstream = (x+3)/5 km

From the given condition, we have,
(x-3)/4-(x+3)/5 = 0
=> (5(x-3)-4(x+3))/20 = 0
=> (5x-15-4x-12)/20 = 0
=> (x - 27)/20 = 0
=> x - 27 = 0
=> x = 27
Therefore speed of boat in still water is 27 km/hr