A motor boat whose speed is 18 km/h in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
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Answered by
5
let speed of stream = x km/hr
Upstream speed ,U = 18 - x
Downstream speed , D = 18 +x
ATQ
24/U - 24/D = 1
24/(18- x) - 24/(18+x) = 1
24*(18+x -18 + x )/(18^2 - x^2) = 1
48x = 324 - x^2
x^2 + 48x -324 =0
x^2 + 54x -6x -324 = 0
x (x+54) -6(x+54) =0
(x-6)*(x+54)= 0
x= 6km/hr
as it can't be negative
Upstream speed ,U = 18 - x
Downstream speed , D = 18 +x
ATQ
24/U - 24/D = 1
24/(18- x) - 24/(18+x) = 1
24*(18+x -18 + x )/(18^2 - x^2) = 1
48x = 324 - x^2
x^2 + 48x -324 =0
x^2 + 54x -6x -324 = 0
x (x+54) -6(x+54) =0
(x-6)*(x+54)= 0
x= 6km/hr
as it can't be negative
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Answered by
3
Given the speed of the boat = 18km/hr
Let the speed of the stream be x km/hr
For upstream
speed = (18-x) km/hr ( speed = distance / time)
distance=24km
= 24/(18-x)
For downstream
= 24/(18+x)
Time upstream = time downstream +1
24/ (18-x) = 24/(18+x) +1
24/(18-x) - 24(18+x) =1
24(18+x) - 24( 18-x) / (18-x) ( 18-x) =1
Taking out the common
24 (18+x - 18+x) / (18+x) (18-x) = 1
24 ( 2x) / (18-x) (18+x) =1
48x / (18 -x) (18+x) =1
48x = (18-x) (18+x)
48x= 18^2 - x^2
48x = 324 - x^2
x^2 + 48x - 324 =0
by comparing with ax^2 +bx+c =0 ( a=1 , b= 48 and c = - 324)
We get d = 3600
by using x= -b + root d / 2a
We get x = 6 and x= -54
x , speed cannot be in negative so the speed is 6 km/hr .
Let the speed of the stream be x km/hr
For upstream
speed = (18-x) km/hr ( speed = distance / time)
distance=24km
= 24/(18-x)
For downstream
= 24/(18+x)
Time upstream = time downstream +1
24/ (18-x) = 24/(18+x) +1
24/(18-x) - 24(18+x) =1
24(18+x) - 24( 18-x) / (18-x) ( 18-x) =1
Taking out the common
24 (18+x - 18+x) / (18+x) (18-x) = 1
24 ( 2x) / (18-x) (18+x) =1
48x / (18 -x) (18+x) =1
48x = (18-x) (18+x)
48x= 18^2 - x^2
48x = 324 - x^2
x^2 + 48x - 324 =0
by comparing with ax^2 +bx+c =0 ( a=1 , b= 48 and c = - 324)
We get d = 3600
by using x= -b + root d / 2a
We get x = 6 and x= -54
x , speed cannot be in negative so the speed is 6 km/hr .
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