# Correct equation for this question

The question is,

A small hydroelectric generating station can produce 17 MWh of energy in 12 months. AFter 4 months of operation, another generator is added. This additional generator can produce 11 MWh in 5 months. How many months after the additional generator was added will it take before the total electrical energy output is 25 MWh?

For an equation we are given

$$(17/12)(t-4)+(11/5)t=25$$

but shouldn't it be switched around to this?

$$(17/12)t+(11/5)(t-4)=25$$

Since the second generator has been working for 4 months less than the first?

Thanks

• Yes, your reasoning is correct. Apr 16, 2014 at 21:13
• You need to specify when you start counting $t$ from. It appears you are counting from the start of the first generator. In that case your equation is correct, but the requested answer is $t-4$ Apr 16, 2014 at 21:44

The question is "How many months after the additional generator was added will it take before the total electrical energy output is 25 MWh?"

That means that you have to give total number of months required to produce 25MWh reduced by 4, but it is better to look at it in a different way.

1. generator works for t+4 months
2. generator works for t months

So it will be:

\begin{align} \frac{17}{12}(t+4)+\frac{11}{5}t=25 \end{align}

• If we use the first formula, and plug in 4 for t, isn't it saying the generator that has already been running for 4 months hasn't produced any power? Since it would be (17/12) times 0? Apr 16, 2014 at 21:23
• You are right, I haven't looked quite enough into it. It should actually be: First generator works for "t+4" months, second one for "t" months. So just put t1=t+4 in th second formula. t1 is the time you want to know. If you use the 2nd formula directly you get the total time, not the time after the instalation of the 2nd generator. Apr 16, 2014 at 21:27
• The $t$ here is measured from the time the second generator is turned on. It is the quantity asked for in the question and corresponds to what Austin calls $t-4$. Both approaches can produce the correct answer. Apr 16, 2014 at 21:46