Question

Sameer can row a certain distance downstream in 24 h and can come back covering the same distance in 36 h. If the stream flows at the rate of 12 km/h, find the speed of Sameer in still water.
a) 30 km/h
b) 15 km/h
c) 40 km/hr
d) 60 km/hr​

Answer 1

Answer:

$\boxed{\sf \;Speed\; of \;Sameer \;in \;still \;water \;is \;12km/hr.}$

Step-by-step explanation:

The time taken by Sameer to row downstream = 24 hr

Time taken for returning upstream = 36 hr

The speed of stream =  12 km/hr

The speed of Sameer in still water = ?

Let the distance he rowed be 'x' km .

Let the speed of  Sameer in still water be , u km/hr.

∴ Case :- 1 (Downstream)

From the question,

$\dfrac{x}{u+12 } = 24$

(Downstream is positive because the current is downstreams)

$x = 24(u-12)$

$\implies$  x = 24u - 288 $\longrightarrow$ (1)

Case :- 2 ( Upstream)

From the question,

$\dfrac{x}{u-12} = 36$

x = 36(u - 12)

x = 36u - 432$\longrightarrow$ (2)

From the questions the distance are equal, So

$\implies$ (1) = (2)

$\implies$ 24u - 288 = 36u - 432

$\implies$ -288+432 = 36u - 24u

$\implies$ 144 = 12u

$\implies u = \dfrac{144}{12} = 12km/hr$

Speed of Sameer in still water is 12km/hr