# With two candles

We have placed two candles of different height in the garden. The longest measures 28 cm and takes 7 hours to consume completely, while the shorter one, which is thicker, takes 11 hours to consume.

We turn on both at the same time when the party starts and after 3 hours, when the friends leave, we turn them off. At that time they are both the same height.

What was the initial length of the shortest candle?

#### Solution

The first candle takes 7 hours to consume, and measures 28 centimeters. That means that every hour burns 28/7 = 4 centimeters. As it is three hours on during the party, when turning off it should measure 12 centimeters less, that is, 16 centimeters.

They tell us that at that time, the candles are equal, so the other candle at that time also measures 16 centimeters. And since its duration is 11 hours, it must still have 8 hours to fully consume, so we deduce that it burns at the rate of 16/8 = 2 centimeters per hour.

Now we can get its height when it was complete: 11 hours by 2 centimeters that burns every hour, they are 22 centimeters what I originally had.