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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?

Sagot :

christian02flz

Answer:

15 minutes

Step-by-step explanation:

ik them and ik the answer

theleangreenbean

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:

[tex]\dfrac{1\hspace{4} office}{30\hspace{4} minutes} \times\dfrac{60\hspace{4} minutes}{1\hspace{4} hour}\\\\\\= \dfrac{1\times 2 \hspace{4}offices}{1\hspace{4}hour}[/tex]

Therefore, Sheldon can paint 2 offices in 1 hour.

Penny:

[tex]\dfrac{1\hspace{4}office}{45\hspace{4}minutes}\times\dfrac{60\hspace{4}minutes}{hour}\\\\\\= \dfrac{1\hspace{4}office}{3}\times\dfrac{4}{hour}\\\\\\= \dfrac{1\times4\hspace{4}offices}{3\hspace{4}hours}\\\\\\= \dfrac{4\hspace{4}offices}{3\hspace{4}hours}\\\\\\=\dfrac{\frac{4}{3}\hspace{4}offices}{hour}[/tex]

Therefore, Penny can paint [tex]\dfrac{4}{3}[/tex] offices in 1 hour.

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

[tex]2+\dfrac{4}{3} = \dfrac{10}{3}[/tex]

Their combined rate is [tex]\dfrac{10}{3}[/tex] offices per hour.

[tex]\dfrac{10}{3}[/tex] offices per hour is the same as [tex]\dfrac{3}{10}[/tex] hours per office (we found the reciprocal).

[tex]\dfrac{3}{10}[/tex] of an hour is equivalent to 18 minutes.

Answer

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

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