Video: Pack 3 • Paper 1 • Question 7

Pack 3 • Paper 1 • Question 7

04:21

Video Transcript

There are 15 boys and 10 girls in an athletics club. The mean time for running the 100 meters for the whole club was 16 seconds. The mean time for the boys was 15 seconds. What was the mean time for the girls?

So the first thing we want to do is actually work out how many people there are in the actual club in total. So we know there’re 15 boys and 10 girls. So therefore, we know that the people in the club is equal to 15 plus 10, which is a total of 25. Okay, great! So we know there are 25 people in the club.

Now for this type of problem, what I like to do is actually break it down into sections. And we use columns to help us do that. So what we can actually say is that, in each column, we’re gonna work out a different part of our question. And that way, we don’t really miss any parts.

So our first column, we’re actually gonna find the sum of the times, which I’m gonna call 𝑇. In the second column, we’re actually gonna work out the sum of the boys’ times, which I only call 𝑡 𝑏. And then in the final column, we’re actually gonna work out the mean time for the girls, because there are the three key parts of this question.

Okay, great! So let’s get on and find the sum of the times of everyone in the club. So first of all, we’ve got this equation here that says that the sum of the times divided by 25 is equal to 16. And that’s because the sum of the times divided by the number of people in the club, which here is 25, is going to be equal to the mean time of all the runners at the club. And here we can see that it’s 16, cause it tells us that in the question.

Okay, great! So now let’s rearrange this to find the sum on the times. So if we multiply each side of our equation by 25, we’re gonna get 𝑇 is equal to 16 multiplied by 25, which is equal to 400 seconds. And just as a quick recap, I’m just gonna show you how you’d actually multiply 16 and 25 on a non-calculator paper. So I’ve actually set up a column multiplication.

So first of all, we multiply six and five, which gives us 30. So we put zero in the units column. And then we carry the three. And then, next, we do five multiplied by one, which gives us five. But then we add on the three that we got from earlier. And then that’s gonna give us eight. And we’re gonna put that in tens column. So there we have 80. Okay, great! So that’s the five multiplied by everything.

Now we’re gonna multiply the two by 16. Well, this time, we actually have two multiplied by six, which actually gives us 12. Well, because it’s 20, because it’s in the tens column multiplied by six, we’re gonna put a zero in the units column. Then we’re gonna put a two in the tens column. And then we will carry the one.

So next, we’re gonna have two multiplied by one or 20 multiplied by 10, which gives us 200 or two. So then we’re gonna add on the one that we carried from earlier. So that gives us three. So we’ve got 320 for the second part.

So now our final stage is to add these together. So we have zero plus zero, which is just zero. Eight plus two is 10. So we put a zero in tens column and carry the one. Then three plus one is equal to four. So we got our total of 400. So great! That’s how you’d work out 16 multiplied by 25 using the column method.

So now we can actually move across and find out the second column, which is the sum of the boys’ times. Well, the sum of the boys’ times divided by 15 is gonna be equal to 15. And that’s because if we have the total sum of the boys’ times, then we divide it by the number of boys, which is 15, cause we can see that from the question.

Then this is gonna be equal to the mean time for the boys, which we know again from the question is 15. So therefore, we can multiply both sides of the equation by 15. So we get the sum of the boys’ times 𝑡 𝑏 is equal to 15 multiplied by 15, which gives us 225 seconds. And again, you could use the column multiplication to help you do this, if it is a non-calculator paper and you didn’t know 15 squared.

Okay, great! So now we can move on to the final column, which is finding the mean time for the girls and actually solving the problem. Well, first of all, so that we can find the mean time for the girls, what we need to know is the sum of the girls’ times, so 𝑡 𝑔. And we know that this is gonna be equal to the total sum of times 𝑇 minus the sum of the boys’ times 𝑡 𝑏, which is gonna be equal to 400 minus 225, because these are the times we found earlier, which gives us a total of 175 seconds.

So therefore, we can say that the mean time for the girls is gonna be equal to the total time for the girls divided by the number of the girls. And again, looking in the question, there are 10 girls. So it’s gonna be 175 divided by 10, which gives us a mean time for the girls of 17.5 seconds.

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