A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the oat in still water and the speed of the stream.
Answers
Answer:
heya hope it helps you good afternoon
Upstream speed is 4 Km/hr
Downstream speed is 8 Km/hr
Speed of boat = 6 Km/hr
Speed of stream = 2 Km/hr
Step-by-step explanation:
Let speed of boat in still water = x km/hr
Let speed of stream = y km/hr
So Upstream speed = (x - y) km/hr
Downstream speed = (x + y) km/hr.
Let 1/x-y = u and 1/x+y = v
Given:
Distance / speed = time.
So 12/x-y + 40/x+y = 8
12u + 40v = 8
Dividing by 4, we get 3u + 10v = 2 -------(1)
16/x-y + 32/x+y = 8
16u + 32v = 8
Dividing by 4, we get 4u + 8v = 2 -------(2)
(1)*4, we get 12u + 40v = 8 --------(3)
(2)*3, we get 12u + 24v = 6 --------(4)
Substracting (4) from (3), we get: 16v = 2
therefore v = 1/8
Substituting v in equation 2, we get 4u + 1 = 2
Therefore u = 1/4
u = 1/x-y = 1/4. Therefore x-y = 4 -------(5)
So upstream speed is 4 Km/hr
v = 1/x+y = 1/8. Therefore x+y = 8. ----------(6)
So downstream speed is 8 Km/hr
Adding 5 & 6, 2x = 12. Therefore x = 6. Speed of boat = 6 Km/hr.
Substituting x = 6 in (5), we get 6 - y = 4, therefore y = 2. Speed of stream = 2 Km/hr.