The current of a stream runs at the rate of 2 km per hr. A motorboat goes 10 km upstream and back again to the starting point in 55 min. Find the speed of the motorboat -

Let the speed of the boat in still water=x km/hr
Speed of the current = 2 km/hr
Then, speed downstream = (x + 2) km/hr
speed upstream = (x - 2) km/hr
Total time taken to travel 10 km upstream and back = 55 minutes
= (55/60) hr
= 11/12 hr.
According to question,
10/(x - 2) + 10/(x + 2) = 11/12
⇒ 120(x+2)+120(x−2) = 11(x² - 4)
⇒ 240x = 11x² - 44
⇒ 11x² - 240x - 44 = 0
⇒ 11x(x -22) + 2(x - 22) = 0
⇒ (x -22) (11x + 2) = 0
Since x cannot be negative.
So, x = 22 km/hr.
Hence, the Speed of the motorboat is 22 km/hr.