In one day, by how much does the distance traveled by the tip of the minute hand exceed the distance traveled by the tip of the hour hand?

In one day, there are 24 hours. In 1 hour, there are 3,600 seconds. So, that means that there are 86,400 seconds. Also, in 1 day, the short hand which denotes the number of hours, makes 2 revolutions around the clock. Its distance traveled would be twice the perimeter of the circle.

Distance traveled by hour hand = 2 (2πr) = 4πr₁

In 60 s, the long hand, which denotes numbers of minutes, makes one revolution around the clock. Since there are 86,400 seconds in a day, that would be a total of 1,440 revolutions.

Distance traveled by minute hand = 1,440 (2πr) = 2,880πr₂

Difference = 2880πr₂ - 4πr₁ = 4π (720r₂ - r₁), where r₁ is the length of hour hand and r₂ is the length of minute hand.