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A man fell into a flooded river and started drowning. Aman saw this from a distance of 300m.  he jumps into the river to rescue the man. Thanks to the river current carrying Aman towards the man, he was saved who would have otherwise died just after 3 minutes. Calculate at what speed Aman swam.

A man fell into a flooded river and started drowning. Aman saw this from a distance of 300m.  he jumps into the river to rescue the man. Thanks to the river current carrying Aman towards the man, he was saved who would have otherwise died just after 3 minutes. Calculate at what speed Aman swam. Correct Answer at least 6 km/hr

Given

distance between Aman and drowning man = 300m

Aman is flowing along with the current.

Time left with Aman to save the man ≤ 3 min

Concept

Aman needs to meet the man within 3 mins to save him. We calculate the speed of Aman such that while going downstream he saves the man.

We use the relative speed concept

When object A is moving with speed S1 in the same direction as object B with speed, S2. Then the relative speed of A to B = S1 – S2  

Calculation

Let the speed of the stream be S

Let Aman’s speed be A

Aman’s speed along with the stream = S + A

As man is drowning, the speed with which he moves = speed of the stream

 Aman’s speed to save the man ≥ distance/time in which man drown

⇒ distance/ relative speed ≤ 3 min

The relative speed of Aman to the man = Aman’s downstream speed – man’s speed

⇒ Aman’s relative speed = A + S –S

⇒ Aman’s relative speed = A

⇒ 300/(A) ≤  3 min

⇒ A ≥ 100 m/min

⇒ A ≥ 100 × 60 /1000 km/hr

⇒ A ≥ 6 km/hr

∴ Aman swam at least at 6 km/hr to save the man.

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