Question

A store sells two kinds of​ candles, scented and unscented. The scented candles burn one eighth inch

in one fourth hour


. The unscented candles burn one ninth inch


in one third hour


. What is the unit rate for inches burned per hour for each kind of​ candle? Which kind of candle burns more in an​ hour? Use pencil and paper. Show how to find the unit rate of hours per inch for each kind of candle. Explain the meaning of this unit rate.

Answer 1

Scented candle, 1/2 inch per hour

Unscented 1/3 inch per hour

Explanation:

The scented candle burns 1/8 inch in every 15 minutes. The unscented candle burns 1/9 inch in every 20 minutes.

We simply first convert the time taken in fraction to minutes for convenience using the conversion 60 minutes are in an hour.

Now let’s calculate unit rate per hour I.e every 60 minutes.

For the scented candle:

1/8 inch burns in 15 minutes

x inch will burn in 60 minutes

To get x, we cross multiply.

1/8 * 60 = 15 * x

15x = 7.5, x = 7.5/15 = 1/2 = 0.5

This means that half of the scented candle will have been burnt in 1 hour.

Now, for the unscented candle, if 1/9 inch burns in 20 minutes, x inch will burn in 60 minutes.

1/9 * 60 = 20x

180x = 60

x = 1/3 or 0.33

This means one-third will be burnt in an hour

The scented one burns more.

The unit rate is the rate of burning per hour. It is the fraction of the candles that will burn per hour. It enables us find the time it will take for either candles to burn up.