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2014-07-12T22:58:02+05:30

This Is a Certified Answer

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Let us take the speed of boat in still water as v1
speed of  stream is v2
in up stream the total relative speed will be v1-v2
in down stream the total relative speed will be v1+v2
According to condition 1
time taken up stream+ time taken down stream = 8hrs
we know distance/speed
(12/v1-v2)+(40/v1+v2)=8@ Equation 1
On solving (52v1-28v2)=8((v1*v1)-(v2*v2))
Keep that aside
now according to condition two 
(12/v1-v2)+(40/v1+v2)=(16/v1-v2)+(32/v1+v2)=8
on solving we get
v1-3v2=0@ Equation 2
Substitute Equation 2 in 1 to get v2 and then v2 in Equation 2 to get v1
final result will be
v1=7.31 Km/hr
v2=2.43 Km/hr
Note: you may notice v2=0 as one of the answers but if v2=0 there is no up stream and down stream
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2014-07-13T12:04:31+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Let  the speed of boat in still water be x
speed of  stream be y
in up stream the speed of boat will be x - y
in down stream the speed of boat will be x + y
so given,
time taken to go up stream+ time taken to go down stream = 8hrs
we know distance/speed

⇒(12/(x - y))+(40/(x +y))=8
On solving (
52x- 28y)=8(x² - y²)

now according to condition two 
(12/(x - y))+(40/(x +y))=(16/(x - y))+(32/(x + y))=8

on solving we get

x - 3y = 0
Substitute Equation 2 in 1 to get x and then y in Equation 2
to get x
final result will be
x = 7.31 Km/hr
y = 2.43 Km/hr

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