A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km down-stream. Determine the speed of the stream and that of the boat in still water.
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A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km down-stream. Determine the speed of the stream and that of the boat in still water.
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and the speed of the strean be y
Then speed of the boat in upstream = (x-y) kmph
The speed of the boat in downstream = (x+y) kmph
Then 30/(x-y) + 44/(x+y) = 10Let 1/(x-y) = a
and 1/(x+y) = bIt implies 30a +44b = 10.......(i)
Similarly 40a+55b = 13........(ii)
Multiplying (i) by 4 and (ii) by 3 we get120a + 176b = 40...........(iii)
120a + 165b = 39..........(iv)Subtracting (iv) from (iii)
we get 44b = 12 Hence b = 1/11Putting b in (i) we get 30a + 4 = 10
Hence a = 1/5Now b = 1/x+y = 1/11or x+y = 11..........(v)and a = 1/x-y = 1/5or x-y = 5...........(vi)Adding (v) and (vi)
we get 2x = 16 Hence x = 8Putting x in (v) we get8+y = 11 Hence y = 3
Hence the speed of the boat = 8kmph
and speed of the stream = 3kmph
Answer:
Speed of stream = 3 km / hr.
Speed of boat in still water = 8 km / hr.
Step-by-step explanation:
Let the speed of the boat in still water be a km / hr and stream be b km / hr
For upstream = a - b
For downstream = a + b
We know :
Speed = Distance / Time
Case 1 .
10 = 30 / a - b + 44 / a + b
Let 1 / a - b = x and 1 / a + b = y
30 x + 44 y = 10 ... ( i )
Case 2 .
13 = 40 / a - b + 55 / a + b
40 x + 55 y = 13 ... ( i )
Multiply by 4 in ( i ) and by 3 in ( ii )
120 x + 176 y = 40
120 x = 40 - 176 y ... ( iii )
120 x + 165 y = 39
120 = 39 - 165 y ... ( iv )
From ( iii ) and ( iv )
40 - 176 y = 39 - 165 y
11 y = 1
y = 1 / 11
120 x = 40 - 176 y
120 x = 40 - 176 / 11
x = 1 / 5
Now :
1 / a - b = 1 / 5
a - b = 5
a = 5 + b ... ( v )
1 / a + b = 1 / 11
a + b = 11
a = 11 - b ... ( vi )
From ( v ) and ( vi )
11 - b = 5 + b
2 b = 6
b = 3
a = 5 + b
a = 5 + 3
a = 8
Hence we get answer.