A person covers 20 km at a speed of 12 km/h and the next 35 km at a speed of…
2019
A person covers 20 km at a speed of 12 km/h and the next 35 km at a speed of 20 km/h. What was the average speed, in km/h, for the whole journey?
Answer: C. 16.1 — CONCEPT Average speed is the total distance travelled divided by the total time taken. When speeds apply to unequal distances, the speeds must not be averaged…
- A.
17.6
- B.
17.2
- C.
16.1
- D.
16.4
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Show answer & explanation
Correct answer: C
CONCEPT
Average speed is the total distance travelled divided by the total time taken. When speeds apply to unequal distances, the speeds must not be averaged directly because the traveller spends different amounts of time on the segments.
APPLICATION
Total distance = 20 + 35 = 55 km.
Time for the first segment = distance ÷ speed = 20 ÷ 12 = 5/3 hours.
Time for the second segment = 35 ÷ 20 = 7/4 hours.
Total time = 5/3 + 7/4 = 20/12 + 21/12 = 41/12 hours.
Average speed = 55 ÷ (41/12) = 55 × 12/41 = 660/41 ≈ 16.10 km/h.
Therefore, the average speed for the whole journey, rounded to one decimal place, is 16.1 km/h.
CROSS-CHECK
Using 16.1 km/h for a 55 km journey gives an implied time of 55 ÷ 16.1 ≈ 3.416 hours, which agrees with 41/12 ≈ 3.417 hours apart from rounding.