Question

a store sells two kinds of candles, scented and unscented. the scented candles burn 1/12 inch in 20 min. the unscented candles burn 1/6 inch in 30 min. which type of candle burns faster in 1 hour and what is its burn rate? the scented candles burn faster, at a rate of 1/4 inch/hr. both candles burn at the same rate of 1/4 inch/hr. the scented candles burn faster, at a rate of 1/3 inch/hr. the unscented candles burn faster, at a rate of 1/3 inch/hr.

Explanation:

Step1: Convert 20 min to hours

Since 1 hour = 60 minutes, 20 minutes is $\frac{20}{60}=\frac{1}{3}$ hours. The scented candle burns $\frac{1}{12}$ inch in $\frac{1}{3}$ hours. To find the rate per hour, we use the formula rate = distance / time. So the rate of the scented candle is $\frac{\frac{1}{12}}{\frac{1}{3}}=\frac{1}{12}\times3 = \frac{1}{4}$ inch per hour? Wait, no, wait, let's check the unscented one. Wait, the unscented candle: the problem says "1/6 inch in 30 min"? Wait, maybe I misread. Wait, the original problem: "The scented candles burn 1/12 inch in 20 min. The unscented candles burn 1/6 inch in 30 min." Let's correct. So 20 min is 1/3 hour, 30 min is 1/2 hour.

Step2: Calculate rate of scented candle

Rate of scented: $\frac{\frac{1}{12}\text{ inch}}{\frac{1}{3}\text{ hour}}=\frac{1}{12}\times3=\frac{1}{4}$ inch per hour? Wait, no, wait, 20 minutes is 1/3 of an hour. So distance is 1/12 inch, time is 1/3 hour. So rate = (1/12) / (1/3) = (1/12)3 = 1/4 inch per hour? Wait, but let's do the unscented. Unscented: 1/6 inch in 30 minutes (which is 1/2 hour). So rate = (1/6) / (1/2) = (1/6)2 = 1/3 inch per hour. Oh! So I made a mistake earlier. So scented: 1/12 inch in 20 min (1/3 hour). So rate = (1/12) / (1/3) = 1/4 inch per hour? Wait, no, (1/12) divided by (1/3) is (1/12)(3/1) = 3/12 = 1/4. Unscented: 1/6 inch in 30 min (1/2 hour). So (1/6) / (1/2) = (1/6)2 = 2/6 = 1/3. So 1/3 is greater than 1/4. So the unscented candle burns faster, at 1/3 inch per hour.

Wait, let's recheck:

Scented: time = 20 min = 1/3 h, distance = 1/12 in. Rate = (1/12) / (1/3) = (1/12)*(3/1) = 3/12 = 1/4 in/h.

Unscented: time = 30 min = 1/2 h, distance = 1/6 in. Rate = (1/6) / (1/2) = (1/6)*(2/1) = 2/6 = 1/3 in/h.

Since 1/3 > 1/4, the unscented candle burns faster at 1/3 in/h.

Step3: Compare the rates

Scented rate: 1/4 in/h, Unscented rate: 1/3 in/h. Since 1/3 > 1/4, the unscented candle burns faster with a rate of 1/3 inch per hour.

Answer:

The unscented candles burn faster, at a rate of 1/3 inch/hr.