Question

Fred and Sally are going to paint a house. Fred knows that if he had to paint the house by himself it would take him 2 times as long as it would take Sally to paint the house by herself. If they work together, they can have the house painted in 24 hours.

What equations could help us determine how long it would take Sally to paint the house on her own?

Answer 1

To determine how long it would take Sally to paint the house on her own, we can set up and solve an equation based on the given information. So, it would take Sally 36 hours to paint the house by herself.

Step-by-step explanation:

To solve this problem, we can start by assigning variables to represent the amount of time it takes each person to paint the house.

Let's say it takes Sally 'x' hours to paint the house by herself.

According to the problem, Fred takes twice as long as Sally, so we can say it takes Fred '2x' hours to paint the house by himself.

If they work together, they can paint the house in 24 hours. We can set up the equation:

1/x + 1/2x = 1/24

To solve this equation, we can multiply every term by the LCD, which is 24x:

24 + 12 = x

36 = x

So, it would take Sally 36 hours to paint the house by herself.