Answer: Speed of boat = 25 km/h
speed of stream = 3 km/h
Step-by-step explanation:
Let x represent the speed of the boat
Let y represent the speed of the stream
Considering downstream,
From the information given, the riverboat travels 56 km downstream in 2 hours. The speed of the river boat while travelling downstream is increased by the stream speed. Thus,
downstream speed = x + y
Distance = speed x time
56 = 2(x + y)
dividing both sides by 2, it becomes
28 = x + y equation 1
Considering upstream,
From the information given, the riverboat travels 66 km upstream in 3 hours. The speed of the river boat while travelling upstream is decreased by the stream speed. Thus,
upstream speed = x - y
66 = 3(x - y)
dividing both sides by 3, it becomes
22 = x - y equation 2
By adding equation 1 and 2, we have
28 + 22 = x + x + y - y
50 = 2x
x = 50/2
x = 25
From equation 1, y = 28 - x
y = 28 - 25
y = 3
Speed of boat = 25 km/h
speed of stream = 3 km/h