SOLUTION: A boat goes 30km upstream and 44kms downstream in 10hrs.In 13hrs it can go 40kms upstream and 55kms downstream.The speed of the boat in still water is?

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Question 1110188: A boat goes 30km upstream and 44kms downstream in 10hrs.In 13hrs it can go 40kms upstream and 55kms downstream.The speed of the boat in still water is?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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A boat goes 30km upstream and 44kms downstream in 10hrs.
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r, boat speed without current
c, speed of current
time, 30%2F%28r-c%29%2B44%2F%28r%2Bc%29=10


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In 13hrs it can go 40kms upstream and 55kms downstream.
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40%2F%28r-c%29%2B55%2F%28r%2Bc%29=13

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The speed of the boat in still water is?
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I did not show a finished solution. Only showed a possible way to start analyzing the description. Two equations in the two unknown variables, r and c.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let speed of boat in still water be x km/h
y the speed of current
x+y = speed with current
x-y = speed against current
time upstream + time down stream = total time

condition I
30/(x-y) + 44/(x+y) = 10
condition II
40/(x-y) + 55/(x+y) = 13
Let 1/(x+y) = a and 1/(x-y) =b
plugging a and b
30b+ 44a = 10
40b + 55a=13
solving the above we get
a= 1/11 and b = 1/5
1/(x+y) = 1/11
1/(x-y) = 1/5
Therefore x+y = 11
x-y = 5
Solve x=8 and y=3 speed in km/h