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Question

A motor boat has a speed of 18 kmhr in still water. It takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.
[3 Marks]

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Solution

Let the speed of the stream be 'x' and the time required to travel upstream be 't'.

Time=DistanceSpeed
[.5 mark]

Speed of boat in upstream
= Speed of boat - Speed of stream
= 18 - x

and, speed of boat in downstream
= speed of boat + speed of stream
= 18 + x [.5 Mark]

From the given data,

t=24(18+x)---------------(1)

t+1=24(18x)------------(2)

Subtracting (1) from (2), we get

1=24[118x118+x]

1=24[2x(182x2)]

182x2=48x

x2+48x182=0 [1 Mark]

Now, the equation x2+48x182=0 can also be written as:

x2+2(24)x+242242182=0

(x+24)2900=0

(x+24)2302= 0

(x+24)2=302

x+24=±30 (Taking square root on both sides)

x=54 or x=6

The speed of the stream cannot be negative.

So, the speed of the stream =6 km/hr
[1 Mark]


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