Rani is swimming speed in still water to the speed of river is 7:1. S…

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