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?

20

Let speed of Boat = a km/h

Speed of Current = b km/h

Downstream Speed = ( a + b) km/h

Upstream speed = (a-b) km/h

According to question ,

Distance = \(\frac{15}{4}\)  km

Time = \(\frac{3}{2}\) hours

Upstream speed =  \(\frac{Distance }{Time }\)

\(\frac{15 × 2 }{3 × 4}\) = 2.5 km/h

(a-b) = 2.5     ------(1)

Now , Downstream speed = \(\frac{Distance }{Time }\)

\(\frac{13 }{2}\) = 6.5 km/h

(a+b) = 6.5      ---------(2)

Adding equation 1 and equation 2

2a = 2.5 + 6.5 = 9

a = 4.5 km/h

So , speed of boat = 4.5 km/h

Time taken to cover 90 km = \(\frac{Distance }{Speed }\) 

= \(\frac{90}{4.5 }\) 

= 20 hours