17) A motor boat covers a certain distance downstream in a river in five hours. It covers the same
distance upstream in five hours and a half. The speed of the water is 2 km/hr. The speed of the
boat in still water is.........
Answers
Let the speed of boat in still water = x km/h
speed of water = 1.5 km/h
Speed of boat downstream = (x+1.5) km/h
time taken in downstream journey = 5 hours
distance travelled = 5(x+1.5) km
Speed of boat upstream = (x-1.5) km/h
time taken in downstream journey = 5.5 hours
distance travelled = 5.5(x-1.5) km
Since same distance is covered in both the cases
5(x+1.5) = 5.5(x-1.5)
⇒ 5x + 5×1.5 = 5.5x - 5.5×1.5
⇒ 5x + 7.5 = 5.5x - 8.25
⇒ 5x - 5.5x = -8.25 - 7.5
⇒ -0.5x = -15.75
⇒ x = (-15.75)/(-0.5)
⇒ x = 31.5 km/h
Hence speed of boat in still water is 31.5 km/h.
Let the speed of the boat in still water is x km/hr.
Then, Speed of boat downstream = (x + 2) km/hr and Speed of boat upstream = (x - 2) km/hr
Distance covered by boat downstream in 5 hours:
= (x + 2) * 2
= (2x + 4) km
Distance covered by boat upstream in 5 (1/2) = (11/2) hours:
= (x - 2) * 11/2
= (11x - 22)/2
By the given condition,
2x + 4 = (11x - 22)/2
=> 2(2x + 4) = 11x - 22
=> 4x + 8 = 11x - 22
=> x = 4.28
Speed of the boat in still water = 4.28 km/hr
Hope it will help!