Question

Cindy and John, working together, can paint the deck in 2 hours. Working alone, John takes twice as long as Cindy. How long does it take Cindy to paint the deck alone?

Answer 1

Answer: it takes Cindy 3 hours to paint the deck alone.

Step-by-step explanation:

Let t represent the number of hours it take Cindy to paint the deck alone. It means that the rate at which she paints the deck per hour is 1/t

Working alone, John takes twice as long as Cindy. It means that the number of hours it takes John to paint the deck is 2t and if he works alone, then the rate at which he paints the deck per hour is 1/2t

By working together, they would work simultaneously and their individual rates are additive. By working together, they can paint the deck in 2 hours. It means that the rate at which they paint the deck together per hour is 1/2. Therefore,

1/t + 1/2t = 1/2

3/2t = 1/2

Cross multiplying, it becomes

2t = 3 × 2 = 6

t = 6/2 = 3 hours