Question
A motorist is pumping gas into his car at a rate of StartFraction 5 over 12 EndFraction of a gallon every StartFraction 1 over 24 EndFraction of a minute. At this rate, how many gallons of gas will he have pumped into his car in One-half of a minute?
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Answers
GPT-4o mini
To determine how many gallons of gas the motorist pumps into his car in half a minute, we start with the given pumping rate:
The motorist pumps \( \frac{5}{12} \) gallons every \( \frac{1}{24} \) minute.
Now, we need to find out how many times \( \frac{1}{24} \) minutes fit into half a minute:
\[
\frac{1}{2} \text{ minute} \div \frac{1}{24} \text{ minute} = \frac{1}{2} \times \frac{24}{1} = 12
\]
This means \( \frac{1}{2} \) minute is equivalent to 12 intervals of \( \frac{1}{24} \) minute.
Next, we multiply the number of intervals by the amount of gas pumped in each interval:
\[
12 \times \frac{5}{12} \text{ gallons} = \frac{12 \times 5}{12} = 5 \text{ gallons}
\]
Thus, the motorist will have pumped **5 gallons** of gas into his car in half a minute.
The answer is **5**.
The motorist pumps \( \frac{5}{12} \) gallons every \( \frac{1}{24} \) minute.
Now, we need to find out how many times \( \frac{1}{24} \) minutes fit into half a minute:
\[
\frac{1}{2} \text{ minute} \div \frac{1}{24} \text{ minute} = \frac{1}{2} \times \frac{24}{1} = 12
\]
This means \( \frac{1}{2} \) minute is equivalent to 12 intervals of \( \frac{1}{24} \) minute.
Next, we multiply the number of intervals by the amount of gas pumped in each interval:
\[
12 \times \frac{5}{12} \text{ gallons} = \frac{12 \times 5}{12} = 5 \text{ gallons}
\]
Thus, the motorist will have pumped **5 gallons** of gas into his car in half a minute.
The answer is **5**.