### Video Transcript

A hydroelectric dam has 28 turbines, each of which has a maximum power output of nine megawatts. The turbines are several decades old however and are to be replaced with newer turbines, which are more efficient and have a higher maximum output power. If each of the newer turbines has a maximum output power of 16 megawatts, by how much does the maximum output power of the power station increase?

Okay, so in this question, we’ve got a hydroelectric dam, which has 28 turbines. Now we we’re told that each turbine has a maximum power output of nine megawatts. Unfortunately, however, these turbines are old. And they need to be replaced with newer ones. The newer ones are more efficient. And they have a higher maximum output power.

Specifically, we’re told that the newer turbines have each a maximum output power of 16 megawatts. And having been given this information, we need to work out by how much the maximum output power of the power station increases. So there are two ways of going about doing this.

Firstly, let’s draw a diagram of the old turbines and the new turbines. Here are the old turbines first of all. We’ve got 28 different turbines. And each one of them has a maximum power output of nine megawatts. And here are the brand spanking new pink turbines, which each have a maximum power output of 16 megawatts. And again, that’s 28 of them because we’re gonna replace the 28 old turbines with 28 new ones.

So the first thing we can do is to work out the maximum total power output when we have the old turbines installed. Well, the total maximum power output is going to be nine megawatts, which is the power output of one turbine, times 28 because that’s 28 of them. And this evaluates to 252 megawatts. That’s the total power output of the power station. And this is before the turbines have been replaced.

After they’ve been replaced, however, the total power output of the power station is 16 megawatts, which is the power of one turbine, times 28. And we can evaluate this to find that the new total power output is 448 megawatts. So clearly, this total power output with the new turbines is larger than what it was before. But how much larger?

Well, the output of the power station has increased by 448 minus 252 megawatts, because this value is going to give us how much the power output has increased by. And this ends up being 196 megawatts.

Now there is a second way of thinking about this. And this way involves thinking about how much extra power each new turbine is generating compared to the old turbine. So each old turbine, which used to produce nine megawatts, is replaced by a new one, which produces 16 megawatts. Therefore, each new turbine produces an extra power of 16 minus nine megawatts, because the old one produced nine and the new one produces 16. So the new one produces an excess of seven megawatts compared to the old one.

And so the total extra power output is simply going to be seven megawatts times 28, because once again we’ve got 28 turbines being replaced. So there are 28 new turbines producing an excess of seven megawatts each. And this, once again, evaluates to 196 megawatts. And so we have our final answer. The maximum output power of the power station increases by 196 megawatts.