Question

A man swims from A to B and back in 4:30 hours.
A block of wood when allowed to go with the stream
from A to B takes 6 hours. What is ratio of the speed
of the man in still water to that of the stream?
(A) 2:1
(B) 3:1
(C) 4:1
(D) 5:1​

Answer 1

Answer:

Let the distance between a and b be denoted by d km

Let speed of stream =u km/hr

wood block is floating, so its speed= speed of stream= u km/hr.

It takes 6 hours to travel from A to B so

d=6u (Distance = Speed x time) [Eqn 1]

Let speed of man be v km/ hr. He takes 4.5 hours for travelling A to B and back

so

d/(v+u)+d/(v-u) = 9/2

Using eqn (1)

6u/(v+u)+6u/(v-u)=9/2

u/(v+u)+u/(v-u) =9/(2 x 6)

u/(v+u)+u/(v-u)=3/4

On both side of equation, we divide the numerator and denominator by u,

we get 1/{(v/u)+1)} +1/{(v/u)-1}=3/4

Let us denote v/u by x we get

1/(x+1)+1/(x-1)=3/4

(x-1)+(x+1)/(x^2–1)=3/4

8x=3x^2–3

3x^2–8x-3=0

(3x+1) (x-3)

as both are v and u represents speed, so none of them can be negative. Hence x=v/ u canot be negative, so we ignore the extraneous solution

and get x=3

or v/u=3

v:u=3:1

Hence Speed of man in still water: Speed of stream =3:1

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