A man swimming in a stream which flows $1 \frac{1}{2}$ km/hr., finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

5 \frac{1}{2} k m / h r

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4 \frac{1}{2} k m / h r

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7 \frac{1}{2} k m / h r

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N o n e o f t h e s e

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Solution

The correct option is B $4 \frac{1}{2} k m / h r$
When he swim with the flow then speed $= (x + \frac{3}{2}) k m / h$
$∴ S_{1} = (x + \frac{3}{2}) \times t$
When he swim against the flow stream then speed $= (x - \frac{3}{2}) t$
$∴ S_{2} = (x - \frac{3}{2}) t$
According to the question,
$S_{1} = 2 S_{2} . (x + \frac{3}{2}) t = 2 (x - \frac{3}{2}) t \Rightarrow (\frac{2 x + 3}{2}) = 2 x - 3 \Rightarrow 2 x + 3 = 4 x - 6 \Rightarrow 9 = 2 x \Rightarrow x = \frac{9}{2} = 4 \frac{1}{2} k m / h r$

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A man swimming in a stream which flows 112 km/hr., finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

The correct option is B 412km/hrWhen he swim with the flow then speed =(x+32)km/h ∴S1=(x+32)×t When he swim against the flow stream then speed =(x−32)t ∴S2=(x−32)t According to the question, S1=2S2.(x+32)t=2(x−32)t⇒(2x+32)=2x−3⇒2x+3=4x−6⇒9=2x⇒x=92=412km/hr

A man swimming in a stream which flows $1 \frac{1}{2}$ km/hr., finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?