Question

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:

Hint:

In upstream–downstream problems: \begin{itemize} \item First find the stream speed using time differences and the given rower’s speed. \item Then apply those speeds to other rowers, using the relation \(\text{time} = \frac{\text{distance}}{\text{speed}}\). \item For round trips, total time is the sum of upstream and downstream times. \end{itemize}

Answer 1

Correct Answer: 8

Step 1: River-speed problems like this usually settle on a whole number, so try \(v=1\) km/h for the current. Sneha's upstream/downstream speeds become \(6-1=5\) and \(6+1=7\) km/h.
Step 2: Check: time upstream for 14 km \(=\frac{14}{5}=2.8\) hours \(=168\) minutes; time downstream \(=\frac{14}{7}=2\) hours \(=120\) minutes. The difference is exactly 48 minutes, confirming \(v=1\) km/h.
Step 3: With \(v=1\), Rita's speeds are \(5-1=4\) km/h upstream and \(5+1=6\) km/h downstream. For a one-way distance \(d\): \(\frac{d}{4}+\frac{d}{6}=\frac{100}{60}=\frac{5}{3}\), giving \(d=4\) km.
\[ \boxed{2\times4 = 8 \text{ km}} \]