A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 6 1/2 hrs. Find the speed of the boat in still water and also speed of the stream.
Answers
Upstream speed is 6 Km/hr
Downstream speed is 14 Km/hr
Speed of boat = 10 Km/hr
Speed of stream = 4 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 24/x-y + 28/x+y = 6
24u + 28v = 6
Dividing by 2, we get 12u + 14v = 3 -------(1)
30/x-y + 21/x+y = 13/2
30u + 21v = 13/2
60u + 42v = 13 ------------(2)
(1) * 5, we get 60u + 70v = 15 --------(3)
Substracting (3) from (2), we get: -28v = -2
therefore v = 1/14
Substituting in equation 1, we get 12u + 1 = 3
Therefore u = 1/6
u = 1/x-y = 1/6. Therefore x-y = 6. -------(4)
So upstream speed is 6 Km/hr
v = 1/x+y = 1/14. Therefore x+y = 14. ----------(5)
So downstream speed is 14 Km/hr
Adding 4 & 5, 2x = 20. Therefore x = 10. Speed of boat = 10 Km/hr.
Substituting x = 10 in (4), we get 10 - y = 6, therefore y = 4. Speed of stream = 4 Km/hr.