anil can row 16 km upstream and 48km downstream in 8hrs. he can row 24 km downstream and 24km upstream in 8hrs. find the speed of the boat in Stillwater and the speed of current
Answers
Speed of the boat in still water = x km/ hr
Speed of the boat in current water =y km/ hr
Speed of the boat in upstream= x- y
Speed of the boat in downstream= x+y
According to the conditions
16/x-y + 48/x+y...........( equation 1 )
24/x-y + 24/x+y..........( equation 2 )
Let
1/ x-y = u
1/x+y = v
16u + 48v = 8......( equation 3 )
24u + 24v = 8.....( equation 4 )
(Eq 4 ) × 2 = 48u + 48v = 8....( equation 5 )
Eq 3 - Eq 4
16u + 48v = 8
48u + 48v= 16
_____________
32u = 8
U= 8/32
U= 1/4.
Put u = 1/4 in eq 3
16 × 1/4 +48v = 8
V = 1/12.
1/x-y = u
×-y =4........( equation 6 )
Similarly..x+y=12....( equation 7 )
Eq 6 + Eq 7
X-y =4
X+y = 12
________
2x = 16
X= 8
Put x = 8 in eq 6
8-y =4
Y= 4
Therefore speed of the boat in still water is 8 km/ hr...
And speed of the boat in current water is 4 km/ hr....
I hope my ans helped ...u ....