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A man completes a journey in 10 hours. He travels the first half at 21 km/h and the second half at 24 km/h. Find the total distance (km).

Difficulty: Medium

Correct Answer: 224 km

Explanation:


Given data

  • Total time = 10 hours
  • First half speed = 21 km/h
  • Second half speed = 24 km/h

Concept / Approach

  • Let total distance be D km. Each half is D/2.
  • Total time = time for first half + time for second half.

Step-by-step calculation

Time = (D/2)/21 + (D/2)/24= D × (1/42 + 1/48)= D × ( (48 + 42) / (42 × 48) ) = D × (90 / 2016)Simplify 90/2016 → divide by 6 ⇒ 15/336; divide by 3 ⇒ 5/112So, Total time = D × (5/112) = 10D = 10 × (112/5) = 224 km

Verification / Alternative

First half time = (112 / 21) = 5 h; second half time = (112 / 24) ≈ 4.6667 h; sum ≈ 9.6667 h? Wait—check halves: Each half = 112 km; times 112/21 ≈ 5.3333 h and 112/24 ≈ 4.6667 h; total = 10 h ✔

Common pitfalls

  • Averaging speeds arithmetically; here halves are equal in distance, not time.
  • Forgetting to split the distance equally and add times.

Final Answer

224 km
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