A boat goes 16km upstream and 24km downstream in 6 Hours. It can go 12km upstream and 36km downstream in the same time. Find the speed of boat in still water and speed of stream.
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Answers
Answer: Speed of boat = 8 kmph and Speed of stream = 4 kmph
Step-by-step explanation:
Let the speed of the boat in still water be X km/hr and the speed of the stream be Y km/hr.
Therefore,
Speed upstream = (X-Y) km/hr
And,
Speed downstream= (X+Y) km/hr.
Time taken to cover 16 km upstream =16/(X-Y) hrs.
Time Taken to cover 24 km downstream = 24/(X+Y) hrs
Total Time Taken to cover to both distance=6 hours.
Therefore,
16/X-Y + 24/X+Y = 6.…...(1)
Again,
Time Taken to cover 12 km upstream= 12/(X-Y) hrs
Time Taken to cover 36 km downstream = 36/(X+Y) hrs.
Total Time Taken to cover both Distance =6 hours.
Therefore,
12/X-Y + 36/X+Y = 6.........(2)
Putting 1/(X-Y) = U and 1/(X+Y) = V in equation (1) and (2). we get,
16U + 24V = 6 => 8U + 12V = 3......(3)
12U +36V = 6 => 2U + 6V = 1.......(4)
On multiplying (4) by 4 and subtracting (3) from it , we get,
12V =1
V = 1/12
Therefore,
1/X+Y = 1/12
X+Y = 12.......(5)
On multiplying (4) by 2 subtracting it from (3) we get,
4U = 1
U = 1/4
Therefore,
1/X-Y = U
1/X-Y = 1/4
X-Y = 4.....(6)
On adding (5) and (6) , we get,
2X= 16
X = 16/2 = 8
On subtracting (4) from (5) , we get,
2Y = 8
Y = 8/2 =4
Hence,
Speed of the boat in still water = 8 Km/ hr
And,
Speed of the stream = 4 km/hr.
Hope it helps.....
Answer:
ur answer is
y=8/2
=4....