Applying rational equations 2 | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

Anya takes 12 hours to paint the deck alone, Bill takes 24 hours, and together they take 8 hours.

Transcript

Working together Anya and Bill stained a large porch deck in 8 hours. Last year Anya stained the deck by herself. The year before Bill painted it by himself, but took twice as long as Anya did. How long did Anya and Bill take when each was painting the deck alone? So let's define some variables here. Let's define A. Let's define A as number of hour... Read More

Key Insights

• 👨‍🎨 Anya takes 12 hours to paint the deck alone.
• 🥡 Bill takes twice as long as Anya, so he takes 24 hours to paint the deck alone.
• 💦 When working together, they are more efficient and complete the task in 8 hours.
• ⏳ Bill's efficiency is lower than Anya's, leading to a longer completion time when he works alone.
• ⌛ Combining their efforts reduces the overall time required to complete the task.
• ☠️ The equation 1/8 = 1/A + 1/B represents the combined rate of Anya and Bill when they work together.
• 🥡 The equation B = 2A represents the relationship between the time it takes Bill and Anya individually.

Questions & Answers

Q: How long does it take Anya to paint the deck alone?

Anya takes 12 hours to paint the deck alone.

Q: How long does it take Bill to paint the deck alone?

Bill takes 24 hours to paint the deck alone.

Q: How long does it take them to paint the deck together?

It takes Anya and Bill 8 hours to paint the deck together.

Q: Why does it take them less time to paint the deck together compared to painting alone?

When they work together, their combined efficiency increases, allowing them to complete the task in a shorter time.

Summary & Key Takeaways

• Anya takes 12 hours to paint the deck alone.

• Bill takes twice as long as Anya, so he takes 24 hours to paint the deck alone.

• When they work together, it takes them 8 hours to paint the deck.