Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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.

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.