satisfied.
Example 19 : A boat goes 30 km
upstream and 44 km downstream in
10 hours. In 13 hours, it can go
air o 40 km upstream and 55 km
down-stream. Determine the speed
of the stream and that of the boat in
still water.
Answers
Answer:
v = 8 kmph and u = 3 kmph
Step-by-step explanation:
Let the speed of the stream be = u kmph
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.