Time, Speed and Distance Question 4 - CAT 2025
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:
Step-by-Step Explanation
Analyze Sneha's River Speeds:
Sneha's still water speed = 6 km/h. Let the river current speed be v km/h.
Upstream speed = 6 − v
Downstream speed = 6 + v
14/(6 − v) − 14/(6 + v) = 48 minutes = 48/60 = 4/5 hour
14 × [2v/(36 − v²)] = 4/5
28v/(36 − v²) = 4/5
35v = 36 − v²
v² + 35v − 36 = 0
(v + 36)(v − 1) = 0
Since current velocity must be positive, v = 1 km/h.
Analyze Rita's Journey:
Rita's still water speed = 5 km/h. Current speed = 1 km/h.
Rita's Upstream speed = 5 − 1 = 4 km/h
Rita's Downstream speed = 5 + 1 = 6 km/h
Let the single-leg distance covered be d km. Total time taken = 100 minutes = 100/60 = 5/3 hours.
d/4 + d/6 = 5/3
d(5/12) = 5/3 ⟹ d = 4 km
Total round-trip distance = 2d = 2 × 4 = 8 km
Correct Answer: 8
💡 FundaMakers Tip:
When solving the upstream-downstream time equation, try small integers for v before solving the full quadratic equation. Knowing that v must cleanly divide the structure layout points to v = 1, which transforms the left side into 14/5 − 14/7 = 2.8 − 2 = 0.8 hours (exactly 48 minutes). This shortcut saves valuable time.