93.
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.
Answer:
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
⇔ 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.
