A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:

Question: A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:

Solution:
Given that,
Swimmer swims 6 min against current and 6 min along current
Distance between P and Q = 120 m

Let,
Speed of swimmer in still water = u m/min
Speed of current = v m/min

Now,
Distance travelled upstream (against current), d₁ = (u - v) × 6
And distance travelled downstream (along current), d₂ = (u + v) × 6

Net displacement from starting point = 120 m
d₂ - d₁ = 120
⇒ 6(u + v) - 6(u - v) = 120
⇒ 6u + 6v - 6u + 6v = 120
⇒ 12v = 120
⇒ v = 120/12
⇒ v = 10 m/min
⇒ v = (10 × 60)/1000
⇒ v = 600/1000
∴ v = 0.6 km/h

So the speed of the current is 0.6 km/h.