A person rows a distance of $$3\frac{3}{4}$$ km upstream in $$1\frac{1}{2}$$ hours and a distance of 13 km downstream in 2 hours. How much time (in hours) will the person take to row a distance of 90 km in still water?

Let speed of boat =  $$x$$ km/hr

and speed of current - $$y$$ km/hr

then upstream = $$(x-y)$$ km/hr

and down stream $$(x+y) $$ km/hr

so according to question $$\dfrac {3\dfrac{3}{4}} {x-y} = 1\dfrac {1}{2}$$

$$\Rightarrow \dfrac {15}{4(x-y)} = \dfrac{3}{2}$$

$$\Rightarrow 2\dfrac{(x-y)}{15} = \dfrac {1}{2}$$

$$\Rightarrow 2(x-y) = 5 $$ 

$$\Rightarrow (x-y) =\dfrac {5}{2}$$  ..... equestion (A)

then down stream $$\dfrac {13}{x+y} = 2 $$

$$\Rightarrow (x+y) = \dfrac{13}{2}$$   ....... equestion (B)

then add equeston (A)+(B) 

then $$2x = \dfrac {18}{2}$$ 

$$x = \dfrac{9}{2} = 4.5 $$ 

put the value $$x = \dfrac{9}{2} $$ in equestion (B)

then $$y = \dfrac {13}{2} -\dfrac{9}{2}$$

$$\Rightarrow y = \dfrac{4}{2}= 2 $$ 

so speed of boat = 4.5 km/hr and current = 2km/hr 

time taken for rowing = 90km/hr 

then = $$\dfrac {90\times 10}{4.5}$$

$$\Rightarrow 20 hr $$ Ans