# 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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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