GATE ECE 2014 Set 3 | GA | Question: 8

Question

A man can row at $8$ $km$ per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in $km$ per hour.

Answer 1

Speed of man $(m) = 8\;km/h$
Let the speed of stream be $s$

According to the question:
Speed of man upstream $= S_1 = m-s$
Speed of man downstream $= S_2 = m+s$

Speed = Distance/Time
Here, since the distance $D$ is same,

$D = S_1 \times T_1 = S_2 \times T_2$

$S_1 \times T_1 = S_2 \times T_2$

$\implies \frac{S_1}{S_2} = \frac{T_2}{T_1} = 1/3$

$m+s = 3(m-s)$

or, $8+s=3(8-s)$

$\implies s=\; 4\;km/h$

Comments

@Shreshta mam, I think we should have $\frac{T_2}{T_1} = \frac{1}{3}$. And then we can get $s = -4$. Where negative sign would indicate velocity in opposite direction.

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Negative sign will not come… that’s a typo.

Answer 2

Time taken in Upstream$=3\times$ Time taken in Downstream

$\dfrac{D}{8-v}=3\times \dfrac{D}{8+v}$

$8+v=24-3v$

$4v=16$

$v=4$

$Ans: 4km/h$