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Each of the two generators produces energy at a constant rate, but the
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23 Jul 2025, 12:50
23 Jul 2025, 12:50
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Each of the two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes?
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Each of the two generators produces energy at a constant rate, but the
[#permalink]
02 Aug 2025, 23:06
02 Aug 2025, 23:06
Expert Reply
Let's analyze the problem step-by-step:
- The first generator produces $n$ units of energy in 4 hours.
- The second generator produces the same $n$ units of energy in half the time, i.e., in 2 hours.
Step 1: Find their rates of energy production.
- Rate of the first generator:
$$
\(\frac{n \text { units }}{4 \text { hours }}=\frac{n}{4} \text { units per hour }\)
$$
- Rate of the second generator:
$$
\(\frac{n \text { units }}{2 \text { hours }}=\frac{n}{2} \text { units per hour }\)
$$
Step 2: Find their combined rate when working simultaneously.
$$
\(\text { Combined rate }=\frac{n}{4}+\frac{n}{2}=\frac{n}{4}+\frac{2 n}{4}=\frac{3 n}{4} \text { units per hour }\)
$$
Step 3: They work simultaneously for 40 minutes.
Since 40 minutes $\(=\frac{40}{60}=\frac{2}{3}\)$ hours.
Step 4: Calculate the total energy produced in 40 minutes.
$$
\(\text { Energy produced }=\text { rate } \times \text { time }=\frac{3 n}{4} \times \frac{2}{3}=\frac{3 n \times 2}{4 \times 3}=\frac{2 n}{4}=\frac{n}{2}\)
$$
Answer: The two generators produce $\(\frac{1}{2}\)$ (one-half) of $n$ units of energy when working simultaneously for 40 minutes.
- The first generator produces $n$ units of energy in 4 hours.
- The second generator produces the same $n$ units of energy in half the time, i.e., in 2 hours.
Step 1: Find their rates of energy production.
- Rate of the first generator:
$$
\(\frac{n \text { units }}{4 \text { hours }}=\frac{n}{4} \text { units per hour }\)
$$
- Rate of the second generator:
$$
\(\frac{n \text { units }}{2 \text { hours }}=\frac{n}{2} \text { units per hour }\)
$$
Step 2: Find their combined rate when working simultaneously.
$$
\(\text { Combined rate }=\frac{n}{4}+\frac{n}{2}=\frac{n}{4}+\frac{2 n}{4}=\frac{3 n}{4} \text { units per hour }\)
$$
Step 3: They work simultaneously for 40 minutes.
Since 40 minutes $\(=\frac{40}{60}=\frac{2}{3}\)$ hours.
Step 4: Calculate the total energy produced in 40 minutes.
$$
\(\text { Energy produced }=\text { rate } \times \text { time }=\frac{3 n}{4} \times \frac{2}{3}=\frac{3 n \times 2}{4 \times 3}=\frac{2 n}{4}=\frac{n}{2}\)
$$
Answer: The two generators produce $\(\frac{1}{2}\)$ (one-half) of $n$ units of energy when working simultaneously for 40 minutes.
gmatclubot
Each of the two generators produces energy at a constant rate, but the [#permalink]
02 Aug 2025, 23:06
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