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A person cycles from home to work at a speed of 8 km/h and reaches 18 minutes late. If he increases his speed to 12 km/h, he reaches 6 minutes early. What is the distance from home to work?

1. 8 km
2. 9.6 km
3. 10 km
4. 12 km

Correct answer: 9.6 km

Solution

At 8 km/h he is 18 minutes late, and at 12 km/h he is 6 minutes early, so the time difference between the two trips is 24 minutes = 0.4 h. Since \(d/8 - d/12 = 0.4\), we get \(d(1/24)=0.4\), hence \(d=9.6\) km.

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