### 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.