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).
Aptitude
Time and Distance
Difficulty: Medium
Choose an option
-
A210 km
-
B224 km
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C240 km
-
D252 km
Answer
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 kmVerification / 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