a boat goes 30 kilometers upstream and 44 km downstream in 10 hours.It can go 40 kilometer upstream and 55 km downstream in 13 hours. find the speed of the boat in still water and that of the stream
Answers
let the speed of the boat be = v kmph
speed upstream will be = v - u kmph
speed downstream will be = v + u kmph
30 km upstream in time duration = 30 / (v - u) hrs
44 km down stream in time duration = 44 / (v + u) hrs
44 / (v + u) + 30 / (v -u) = 10 hrs --- (1)
Similarly,
40 /(v - u) + 55 / (v +u) = 13 hrs Multiply with 3/4:
30/(v-u) + 165 / 4(v+u) = 39/4 --- (2)
Now (1) - (2) => [44 - 165/4] / (v+u) = 10 - 39/4 = 1/4
=> v + u = 11 --- (3)
Substitute this in (1) to get:
44/11 + 30/(v-u) = 10
=> v - u = 30/6 = 5 --- (4)
Solving (3) and (4) , we get : v = 8 kmph and u = 3 kmph
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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.