Max completes his journey at an average speed of 9 km/h. He covers the first 9…
2023
Max completes his journey at an average speed of 9 km/h. He covers the first 9 km at a speed of 6 km/h and takes 1.5 hours to cover the remaining distance. Find the speed at which he covered the remaining distance.
- A.
11 km/h
- B.
12 km/h
- C.
13 km/h
- D.
14 km/h
Show answer & explanation
Correct answer: B
Concept
The average speed for an entire journey is total distance divided by total time, not a simple average of the individual speeds. When one segment's speed and the other segment's time are known along with the overall average speed, first find the total time, express the total distance in terms of the unknown speed, and then apply the average-speed formula to solve for it.
Application
Let the speed for the remaining distance be x km/h.
Time for the first 9 km at 6 km/h = 9/6 = 1.5 hours.
Total time for the journey = 1.5 + 1.5 = 3 hours, since the remaining distance also takes 1.5 hours.
Total distance = 9 km (first part) + 1.5x km (remaining part, since distance = speed x time).
Using average speed = total distance / total time: (9 + 1.5x)/3 = 9.
Solving: 9 + 1.5x = 27, so 1.5x = 18, giving x = 12.
Cross-check
With x = 12 km/h, the remaining distance = 1.5 x 12 = 18 km, so total distance = 9 + 18 = 27 km over 3 hours. This gives 27/3 = 9 km/h, matching the given average speed.