A boat travels from point A to point B downstream and then returns upstream to…
2026
A boat travels from point A to point B downstream and then returns upstream to A. The boat spends 10 hours on the entire round trip, including a 30-minute stop caused by engine trouble during the upstream return. If its speed in still water is 20 km/h and the stream speed is 5 km/h, find the effective average speed for the entire journey, rounded to the nearest integer.
Answer: C. 18 — ConceptFor motion with a stream, downstream speed equals the still-water speed plus the stream speed, while upstream speed equals the still-water speed minus…
- A.
20
- B.
14
- C.
18
- D.
16
Attempted by 20 students.
Show answer & explanation
Correct answer: C
Concept
For motion with a stream, downstream speed equals the still-water speed plus the stream speed, while upstream speed equals the still-water speed minus the stream speed. Average speed for the complete trip is total distance divided by total elapsed time, so a stoppage contributes time but no distance.
Application
Compute the downstream speed: 20 + 5 = 25 km/h.
Compute the upstream speed: 20 - 5 = 15 km/h.
Let the one-way distance be d km. The moving time is 10 - 0.5 = 9.5 hours.
Form the time equation: d/25 + d/15 = 9.5.
Combine the fractions: d(3/75 + 5/75) = 9.5, so 8d/75 = 9.5.
Solve for the one-way distance: d = 9.5 × 75/8 = 89.0625 km.
The total distance is 2d = 178.125 km, and the total elapsed time is 10 hours.
Cross-check
Using d = 89.0625 km, the downstream time is 3.5625 hours and the upstream time is 5.9375 hours. These add to 9.5 hours; adding the 0.5-hour stop gives the stated 10 hours.
Result
The effective average speed is 178.125/10 = 17.8125 km/h, which rounds to 18 km/h.