Question

a 10 - inch candle burns at a rate of 1.2 inches an hour. how many hours must the candle burn until it is less than 1 inch tall?

Explanation:

Step1: Determine the amount to burn

The candle starts at 10 inches and we need it to be less than 1 inch, so the amount it needs to burn is at least \(10 - 1=9\) inches.

Step2: Calculate time using rate

The rate is 1.2 inches per hour. Let \(t\) be the time in hours. We know that \(\text{distance}=\text{rate}\times\text{time}\), so \(t = \frac{\text{distance}}{\text{rate}}\). Substituting the distance (9 inches) and rate (1.2 inches per hour), we get \(t=\frac{9}{1.2}\).

Step3: Solve the division

\(\frac{9}{1.2}=\frac{90}{12} = 7.5\) hours. Since we need it to be less than 1 inch, we need to burn at least 7.5 hours.

Answer:

7.5 hours (or more precisely, any time \(t\) where \(t\geq7.5\) hours)