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

Let the river speed be v km/h. For Sneha still-water speed = 6 km/h:

Upstream speed = (6-v), downstream speed = (6+v).

Given $$\frac{14}{(6-v)}-\frac{14}{(6+v)}=48$$minutes =0.8 hours. 

So, $$\frac{14(6+v-6+v)}{36-v^2}=0.8 \Rightarrow \frac{28v}{36-v^2}=0.8$$

$$28v=0.8(36-v^2)=28.8-0.8v^2 \Rightarrow 0.8v^2+28v-28.8=0$$

Multiply by 5: $$4v^2+140v-144=0$$

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

We get v = 1

Thus, the river speed is 1 km/h. For Rita, the still water speed is 5 km/h:
Upstream speed = 5-1=4 km/h, Downstream Speed = (5+1=6) km/h.

If she rows d km upstream and returns d km downstream, the total time

$$ \frac{d}{4}+\frac{d}{6}=d\Big(\frac{1}{4}+\frac{1}{6}\Big)=d\cdot\frac{5}{12}\ \text{hours}$$

This equals 100 minutes $$=100/60=\dfrac{5}{3}$$ hours. 

So, $$d\cdot\frac{5}{12}=\frac{5}{3}\ \Rightarrow\ d=4\ \text{km}$$

Total distance covered 2d=8 km.