A boatman goes 80 km upstream and downstream in 6 hours. Time taken to go 5 km downstream is equal to time taken to go 4 km upstream. Find the speed of boat in still water (in km/hr).

27

Let the speed of boat = x km/hr

the speed of current = y km/hr

Speed of boat in downstream = (x + y) km/hr

Speed of boat in upstream = (x - y) km/hr

Now, ATQ

\(\frac{5}{x + y}\) = \(\frac{4}{x - y}\)

5x - 5y = 4x + 4y

x = 9y

x : y = 9 : 1

Hence,

\(\frac{80}{x + y}\) + \(\frac{80}{x - y}\) = 6

\(\frac{80}{10R}\) + \(\frac{80}{8R}\) = 6

1R = 3

Speed of boat = 9 x 3 = 27 km/hr