Question

A man can swim with a speed of $4.0{\text{kmh}}^{-1}$ in still water. How long does he take to cross a river $1.0\text{km}$ wide if the river flows steadily at $3.0{\text{kmh}}^{-1}$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

Answer 1

Step 1: Draw rough sketch of given situation.

Given speed of man in still water $=4\text{km/h}$
Width of river = 1 km
Speed of river flow $=3\text{km/h}$

Step 2: Final time taken to cross the river.
Given,
Speed of the man, $v_m=4\text{km/h}$
Width of the river $=1\text{km}$
Time taken to cross the river $t=\frac{\text{width of the river}}{\text{speed of the man}}$
$t=\frac{1}{4}hr$
$=\frac{60}{4}\text{min}=15\text{min}$

Step 3: Final distance along the river.
As the man makes his strokes normal to the river current.
So, distance covered along the river
= speed of river $\times$ taken by the man to reach other bank
$=3km/h\times \frac{1}{4}hr$
$=0.75\text{km}$ or $750m$.

Final Answer: The man takes 15 min to cross the river and he goes 750 m down the river when he reaches the other bank.