Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is

Entered answer:

✅ Correct Answer: 8

Let the river's speed $= v$ km/h

Sneha's upstream speed $= (6 - v)$ km/h

Sneha's downstream speed $= (6 + v)$ km/h

Sneha takes 48 minutes more upstream than downstream to cover 14 km:

$\dfrac{14}{6 - v} - \dfrac{14}{6 + v} = \dfrac{48}{60} = \dfrac{4}{5}$ hours

$14\left(\dfrac{(6+v) - (6-v)}{(6-v)(6+v)}\right) = \dfrac{4}{5}$

$\dfrac{28v}{36 - v^2} = \dfrac{4}{5}$

$140v = 144 - 4v^2$

$4v^2 + 140v - 144 = 0$

$v^2 + 35v - 36 = 0$

$(v + 36)(v - 1) = 0$

$v = 1$ km/h (since speed cannot be negative)

Rita goes upstream a distance $d$ km, then returns downstream the same distance $d$ km.

Rita's upstream speed $= 5 - 1 = 4$ km/h

Rita's downstream speed $= 5 + 1 = 6$ km/h

Total time $= 100$ minutes $= \dfrac{5}{3}$ hours

$\dfrac{d}{4} + \dfrac{d}{6} = \dfrac{5}{3}$

$\dfrac{3d + 2d}{12} = \dfrac{5}{3}$

$\dfrac{5d}{12} = \dfrac{5}{3}$

$d = \dfrac{5}{3} \times \dfrac{12}{5}$

$d = 4$ km

Total distance $= d + d = 4 + 4 = 8$ km

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