A man starts from his home towards his office at a speed of $5$ m/s. After every $10$ minutes, he increases his speed by $5$ m/s and thus reaches his office after $1$ hour. What is the distance between his home and his office?

The 1 hour duration divided by 10 minute intervals gives 6 equal time intervals, meaning he walks at 5 m/s, 10 m/s, 15 m/s, 20 m/s, 25 m/s and 30 m/s for 10 minutes each. Converting 10 minutes to seconds gives 600 seconds, so the distances covered in the intervals are 3000 m, 6000 m, 9000 m, 12000 m, 15000 m and 18000 m. Summing these gives a total distance of 63000 m, which equals 63 km.

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