Question : A man covered a distance of 42 km in 5 hours. He covered part of the journey on foot at a speed of 6 km/h and part of the journey by bicycle at a speed of 10 km/h. How much distance did he walk on foot?
Option 1: 18 km
Option 2: 15 km
Option 3: 10 km
Option 4: 12 km
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Correct Answer: 12 km
Solution :
Total distance = 42 km
Total time = 5 hours
Speed when he travelled on foot = 6 km/h
Speed when he travelled on bicycle = 10 km/h
Time = $\frac{\text{Distance}}{\text{Speed}}$
Let the distance travelled on foot be $d$.
Time taken on foot + Time taken on bicycle = Total time taken
⇒ $\frac{d}{6} + \frac{(42 – d)}{10} = 5$
⇒ $\frac{d × 5 + 3 × (42 – d)}{30} = 5$
⇒ $5d + 126 - 3d = 5 × 30$
⇒ $2d + 126 = 150$
⇒ $d = 12$ km
$\therefore$ The distance travelled on foot is 12 km.
Hence, the correct answer is 12 km.
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