Bunuel wrote:
The XYZ river flows at 12 km/hr. A boy who can row at 25/18 m/s in still water had to cross it in the least possible time. The distance covered by the boy is how many times the width of the river XYZ?
A. 2.1
B. 2.3
C. 2.6
D. 2.9
E. 3.0
Are You Up For the Challenge: 700 Level QuestionsResponding to a PM.
Let us convert the speeds in same units.
Now, 1 m/s is 18/5 km/h => \(1 m/s = \frac{\frac{1}{1000}}{\frac{1}{3600}}km/hr = \frac{3600}{1000}=\frac{18}{5}\)km/h
Thus, the speed of the boy is \(\frac{25}{18}m/s = \frac{25}{18}*\frac{18}{5}=5\)km/hr
Next, let us visualize the boat's movement due to different movements.
Boys rowing speed: This will take the boy straight across the river if acting alone.
Water speed: This will take the boy down the river if acting alone.
So, we have one force taking him across and the other down, that is it makes a L shape, where vertical line of L is the width covered by boy and horizontal line in L covered by river.
When these two forces are combined, the boy will move obliquely from the open end in north to the open end in east of 'L'.
Thus we are looking at a Right angled triangle, one side of which is covered by boy and other side by river, resulting in boy moving along the hypotenuse, so speed = \(\sqrt{12^2+5^2}=13\)
The ratio of speeds will give you the ratio of distance covered => Final speed:boy's speed = Hypotenuse : width of river = 13:5 or 2.6:1