Rani is swimming speed in still water to the speed of river is 7:1. She swims 4.2 km up the river in just 14 min. How much time will Rani take to swim 18.4 km down the river?

46 Min

Let,

Speed of boat in still water - x

Speed of stream/current - y

Upstream speed: x - y

Downstream speed: x + y

According to the question:

Ratio of x: y = 7: 1

Upstream speed = \(\frac{4200 }{\text{840} }\) = 5 m/s

So, x - y = 6 parts, 6 parts → 5 m/s then value of 1 part → \(\frac{5 }{6 }\) i.e. y = \(\frac{5 }{6 }\) m/s and x = \(\frac{5 }{6 }\) x 7 = \(\frac{35 }{6 }\) m/s

We know that, 

Speed = \(\frac{ Distance}{ Time}\)

Downstream speed = \(\frac{35 }{6 }\) + \(\frac{5 }{6 }\) = \(\frac{20 }{3 }\) m/s

So, putting values in the formulae:

\(\frac{20 }{3 }\) = \(\frac{18400}{ Time}\)

Time = \(\frac{18400}{ \frac{20 }{3 }}\)

Time = \(\frac{\text{18400 x 3}}{ 20}\)

Time = 2760 seconds = 46 minutes