A person covered 42 kilometres in 5 hours using both walking and cycling. Walking speed was 6 km/h and cycling speed was 10 km/h.…

Question

A person covered 42 kilometres in 5 hours using both walking and cycling. Walking speed was 6 km/h and cycling speed was 10 km/h. What distance did they cover by walking?

1. A. 12 km (Correct answer)
2. B. 1.2 km
3. C. 37 km
4. D. 3.9 km

Correct Answer

Option A — 12 km

Detailed Solution & Explanation

The correct answer is 12 km.

Key Points

• This is a classic two-part motion problem solved with a single linear equation.
• Let the walking time = t hours, so the cycling time = (5 − t) hours (total time is 5 hours).
• Distance = speed × time, and the total distance is 42 km:
• 6t + 10(5 − t) = 42
• 6t + 50 − 10t = 42 → −4t = −8 → t = 2 hours.
• Therefore the distance walked = speed × time = 6 × 2 = 12 km.
• Verification: cycling = 10 × 3 = 30 km; 12 + 30 = 42 km ✓.
• whenever a total distance is covered in two modes with different speeds over a known total time, set the time of one part as t and the other as (total − t), then form one equation.

Exam Tip

• you can also use alligation on speeds, but the single-variable method is the most reliable here.