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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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
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