# A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. find the speed of the board in still water and the speed of the stream.

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by jhontu

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by jhontu

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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 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

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

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

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