A person walks 5 km to a destination in 1 hour. On the return journey, they walk the same 5 km distance back to the starting point in 30 minutes. What is the average speed of the person for the entire journey?
- (a)6.67 km/h
- (b)7.5 km/h
- (c)8 km/h
- (d)10 km/h
Answer
Why
Correct — A.
Rule: average speed = total distance ÷ total time.
Total distance = 5 + 5 = 10 km
Total time = 1 h + 30 min = 1.5 h
Average speed = 10 ÷ 1.5
= 20⁄3 = 6.67 km/h → option (a)
Why the others are wrong
- (b)7.5 km/h — 7.5 km/h is the plain average of the two speeds, (5 + 10) ÷ 2. The walker spends 1 hour at 5 km/h but only half an hour at 10 km/h, so the slower speed weighs more.
- (c)8 km/h — 8 km/h would mean the 10 km took 10 ÷ 8 = 1.25 hours. The two legs take 1 hour and 30 minutes, which is 1.5 hours.
- (d)10 km/h — 10 km/h is the return speed alone, 5 km in half an hour. The slower outward leg at 5 km/h pulls the average for the whole trip well below it.
Concept
Average speed is not the average of the speeds. It is total distance over total time, so the leg you spend longer on counts for more.
For equal distances at speeds x and y, the formula reduces to 2xy ÷ (x + y). Here 2 × 5 × 10 ÷ (5 + 10) = 100 ÷ 15 = 6.67 km/h, the same answer by a shorter route.
The item sits in the Reasoning section but is a speed calculation. The working is the same as in Quant.
Key facts
- Average speed = total distance ÷ total time.
- Equal distances at speeds x and y give an average speed of 2xy ÷ (x + y).
- 30 minutes is 0.5 hour, so the round trip takes 1.5 hours.
Study next
Common traps
- Averaging the two speeds to get 7.5 km/h.
- Writing 1 h 30 min as 1.3 h, which gives 10 ÷ 1.3 ≈ 7.7 km/h.
The equal-distance rule is also tested at 26 Sep 2025, 12:30, Quant Q.16: 100 km at 50 km/h then 100 km at 25 km/h, keyed 33.33 km/h, with the plain average 37.5 km/h among the wrong options.
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