Question

Marcos, David, and Jacob are each going to paint a room individually. It takes Marcos 8 hours, David 5 hours, and Jacob f hours. Write and simplify a rational expression showing the total amount of time it takes to paint the room if all three work together.​

Answer 1

• 40f / (13f + 40) hours

Explanation:

• Marcos can paint 1/8 part of the room in 1 hour,
• David can paint 1/5 part,
• Jacob can paint 1/f part

Together they can paint in 1 hour:

• 1/8 + 1/5 + 1/f part of the room

Let them complete the painting in x hours.

The expression we need is:

• 1/8 + 1/5 + 1/f = 1/x
• (5f + 8f + 40)/40f = 1/x
• (13f + 40) / 40f = 1/x
• 40f / (13f + 40) = x