A boat can go 30 km downstream and 24 km upstream in 2 hours 27 mins. Also it can go 10 km downstream and 4 km upstream in 37 mins. What is the speed of the boat upstream (in km/hr)?

20

Let speed of Boat in still water = u km/hr

speed of stream = v km/hr

ATQ,

⇒ \(\frac{30}{u\;+\;v}\) + \(\frac{24}{u\;-\;v}\) = 147 min  ....(i)

⇒ \(\frac{10}{u\;+\;v}\) + \(\frac{4}{u\;-\;v}\) = 37 min  ....(ii)

multiply ii by 3 and subtract from (i)

We get,

\(\frac{12}{u\;-\;v}\) = 36 min = \(\frac{36}{60}\) hrs

⇒  (u - v) = \(\frac{12\;×\;60}{36}\) = 20 km/hr