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?
Answer & explanation
Correct answer: option 2
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