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a boat goes 12 km upstream and 40 km downstream in 8hrs. it can go 16km upstream and 32 km downstream in the same tym. find speed of the boatin still water and speed off stream...?
a boat goes 12 km upstream and 40 km downstream in 8hrs. it can go 16km upstream and 32 km downstream in the same tym. find speed of the boatin still water and speed off stream...?
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Let the speed of the boat downstream = y.
Given that A boat goes 12km upstream and 40km downstream in 8 hours.
12/x + 40/y = 8
96/x + 320/y = 64 ----- (1)
Given that A boat goes 16km upstream and 32km downstream in same time.
16/x + 32/y = 8
96/x + 192/y = 48 ------- (2)
On solving (1) & (2), we get
96/x + 320/y = 64
96/x + 192/y = 48
--------------------------------
128/y = 16
128 = 16y
y = 8.
Substitute y = 8 in (1), we get
96/x + 320/y = 64
96/x + 40 = 64
96/x = 64 - 40
96/x = 24
96 = 24x
x = 4.
Therefore boat upstream speed x - y = 4km/hr.
boat downstream speed x +y = 8km/hr.
On solving above equations, we get
x - y = 4
x + y = 8
-------------
2x - 12
x = 6.
Substitute x = 6 in above, we get
x + y = 8
6 + y = 8
y = 2.
therefore speed of the boat in still water = 6km/hr and off stream = 2km/hr.
Hope this helps!
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Heya!!! ✌️✌️________________^_^
Here is your answer dear........
let speed of boat is x and stream is y
speed of boat upstream = x-y
speed of boat downstream = x+y
8 = 12/(x-y) + 40/(x+y)
8(x²-y²) = 52x -28y ..................(1)
8 = 16/(x-y) + 32/(x+y)
8(x²-y²) = 48x - 16y ..................(2)
(1) - (2)
4x - 12y = 0
x = 3y .........................(3) put in equation (1)
8(9y²-y²) = 52*3y - 28y
64y² = 128y
y = 0 or 2
y= 0 not possible
put y = 2 in equation (3)
x = 6Km./h (speed of boat in still water)
y = 2Km./h (speed of stream)
I HOPE THIS WILL HELP YOU OUT.....
HAVE A GREAT DAY DEAR....
#Bhavana ☺️