Question

Sheldon can paint an office in 30 min and Penny can paint an office

in 45 min. How long would it take them to paint one office working together?

Answer 1

Key Ideas

• Addition with rates

Solving the Problem

We're given:

• Sheldon can paint 1 office in 30 minutes
• Penny can paint 1 office in 45 minutes

First, convert both the given rates to offices per hour instead of per minutes.

Sheldon:

`\frac{1\hspace{4} office}{30\hspace{4} minutes} *\frac{60\hspace{4} minutes}{1\hspace{4} hour}\\\\\\= \frac{1* 2 \hspace{4}offices}{1\hspace{4}hour}`

Therefore, Sheldon can paint 2 offices in 1 hour.

Penny:

`\frac{1\hspace{4}office}{45\hspace{4}minutes}*\frac{60\hspace{4}minutes}{hour}\\\\\\= \frac{1\hspace{4}office}{3}*(4)/(hour)\\\\\\= \frac{1*4\hspace{4}offices}{3\hspace{4}hours}\\\\\\= \frac{4\hspace{4}offices}{3\hspace{4}hours}\\\\\\=\frac{(4)/(3)\hspace{4}offices}{hour}`

Therefore, Penny can paint
`(4)/(3)` offices in 1 hour.

To find their rate working together, add their individual rates:

`2+(4)/(3) = (10)/(3)`

Their combined rate is
`(10)/(3)` offices per hour.

`(10)/(3)` offices per hour is the same as
`(3)/(10)` hours per office (we found the reciprocal).

`(3)/(10)` of an hour is equivalent to 18 minutes.

Answer

It would take them 18 minutes to paint one office working together.