# A boat, which has a speed of 5km/h in still water, crosses a river of width 1km along the shortest path possible in 15 minutes. Find the velocity of the river?

Speed in still water is 5 km/h

Let the velocity of the river be m km/h

Width of the river is 1 km and time taken is 15 minutes, that is 14 hours.

Using the formula, d = s×t

d = 5 × 14 = 1.25km

If the river had been still, the boat would have moved from A to B, 1 km but, the boat moves from A to C

⇒ CB2 = AC2−AB2

⇒ CB2 = 1.252−12

⇒ CB2 =0.5625

∴CB = 0.75

The covered distance by the river water in 15 minutes is 0.75km.

Now, the velocity of the river is

v = d/t = 0.75/1/4 =3km/h

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