Question

The diameter of the clock face of Big Ben in London measures 29 feet. The minute hand is 14 feet long and the hour hand is 9 feet long. As the minute hand moves from 12 to 5, how many more feet does it travel than the hour hand as it moves from 12 to 5?

Answer 1

13 feet

Explanation:

The first step in determining the distance each hand moves is to determine the angle their movement form, going from 12 to 5.

From 12 to 5, that represent a movement of 5... out of a possible movement of 12 (to reach 12 again)... so their movement is equal to 5/12 of a circle.

Now that we have the fraction of the circle we need, we can calculate the distance run by each hand. We'll start with the minute hand, which is 14 feet long.

The length of the arc of a full circle is calculated by the formula 2 * π * r where r is the radius of the circle. In our case, the radius of the circle is the length of the hand drawing the circle. And since we don't want to know the all the circumference of the circle, but only the 5/12 of it, representing the movement from 12 to 5, we'll factor it in:

`d = (5)/(12) * 2 * \pi * 14 = 36.63`

Now, let's do the same calculation for the hour hand which measures 9 feet:

`d = (5)/(12) * 2 * \pi * 9 = 23.55`

The difference is then 36.63 - 23.55 = 13.08 feet.

Which we round down to 13 feet.