Question

A painter can paint 27 of a room in 1 hour. How long will it take to paint 1 12 rooms?

Answer 1

To find out how long it will take to paint \(1 \frac{1}{2}\) rooms, we first convert the mixed number to an improper fraction:

\[
1 \frac{1}{2} = \frac{3}{2} \text{ rooms.}
\]

Since the painter can paint \(\frac{2}{7}\) of a room in 1 hour, we need to determine how many hours it will take to paint \(\frac{3}{2}\) rooms.

Let \(x\) be the number of hours it takes to paint \(\frac{3}{2}\) rooms. The painter's rate is:

\[
\frac{1 \text{ room}}{27 \text{ hours}}.
\]

Hence, the painter paints \( \frac{1}{27} \) of a room per hour. Therefore, in \(x\) hours, the painter paints:

\[
\frac{x}{27} \text{ rooms.}
\]

To find the time needed to paint \(\frac{3}{2}\) rooms, we set up the equation:

\[
\frac{x}{27} = \frac{3}{2}.
\]

Now, solve for \(x\):

\[
x = \frac{3}{2} \times 27.
\]

Calculating \(x\):

\[
x = \frac{3 \times 27}{2} = \frac{81}{2} = 40.5 \text{ hours.}
\]

Thus, it will take the painter **40.5 hours** to paint \(1 \frac{1}{2}\) rooms.