### Video Transcript

Matthew sweeps two-ninths of the
hall floor in 15 minutes, or one-quarter of an hour. What fraction of the floor does he
sweep in one hour? And how long does it take for him
to sweep the whole floor?

We’ve been given this really
helpful diagram. Our bottom line is the time and our
top line is how much of the floor has been swept in that same amount of time. In one-fourth of an hour,
two-ninths of the hall was swept. And that means every fourth of an
hour, two-ninths of the floor can be swept. Two-ninths plus two-ninths will be
four-ninths. In half an hour, four-ninths of the
floor can be swept. And then by that measure, in
three-fourths of an hour, six-ninths of the floor can be swept. And then, in one hour, eight-ninths
of the floor can be swept.

Our first question asked, what
fraction of the floor does he sweep in one hour? And we found that to be
eight-ninths. The second question might not feel
as straightforward. How long does it take for him to
sweep the whole floor? If we continue out our line a
little bit, there is some point where nine-ninths of the floor is swept. And that value is going to be a bit
longer than an hour. Now, nine-ninths is one-ninth more
than eight-ninths. So one thing that would be helpful
for us to find out is how long does it take for Matthew to sweep one-ninth of the
floor.

Because these values are
proportional, we know that one-ninth is half of two-ninths, and that means it will
take half of one-fourth to sweep one-ninth of the floor. Half of one-fourth is
one-eighth. What we’re saying here is one-ninth
of the floor is swept every one-eighth hour. If we wanted to get nine-ninths of
the floor swept, we would multiply the numerator one-ninth by nine. And because these values are
proportional, we’ll need to multiply the one-eighth of an hour by nine as well,
which gives us nine-eighths of an hour for the whole floor swept. Nine-eighths of an hour is one and
one-eighth. And so we can say it would take
Matthew one and one-eighth of an hour to sweep the whole floor, which is 67 and a
half minutes.