A man can row three-quarters of a kilometre against the stream in 11¼ minutes…
2023
A man can row three-quarters of a kilometre against the stream in 11¼ minutes and downstream in 7½ minutes. What is his speed in still water, in km/h?
Answer: C. 5 — Concept Let u be the speed in still water and s the stream speed. Downstream speed is u + s, while upstream speed is u − s. Therefore, the still-water speed…
- A.
7
- B.
6
- C.
5
- D.
8
Attempted by 154 students.
Show answer & explanation
Correct answer: C
Concept
Let u be the speed in still water and s the stream speed. Downstream speed is u + s, while upstream speed is u − s. Therefore, the still-water speed is half the sum of the downstream and upstream speeds. For each direction, speed equals distance divided by time after using consistent units.
Application
The distance is ¾ km = 0.75 km. Convert the times to hours: 11¼ minutes = 11.25/60 hour = 0.1875 hour, and 7½ minutes = 7.5/60 hour = 0.125 hour.
Upstream speed = 0.75/0.1875 = 4 km/h.
Downstream speed = 0.75/0.125 = 6 km/h.
Hence u = (upstream speed + downstream speed)/2 = (4 + 6)/2 = 5 km/h.
Cross-check
The stream speed is s = (6 − 4)/2 = 1 km/h. Then u − s = 5 − 1 = 4 km/h and u + s = 5 + 1 = 6 km/h, matching the two measured speeds.
Result: the speed in still water is 5 km/h.