Question

Andrew can paint the neighbors house 3 times as fast as Bailey. The year Andrew and Bailey worked together, it took them 4 days. How many days would it take each of them to paint the house?

Answer 1

Andrew would take approximately 16 days to paint the house alone, while Bailey would take approximately 5.33 days. When they work together, it takes them 4 days to complete the job.

Step-by-step explanation:

To solve this problem, we can assign variables to represent the time it takes for Andrew and Bailey to paint the house individually. Let's say Andrew takes x days and Bailey takes y days. According to the problem, we know that Andrew can paint the house 3 times as fast as Bailey. This can be expressed as:

x = 3y

Also given is that when they work together, it takes them 4 days to paint the house. This means that their combined work rate is equivalent to 1/4 of the house painted per day:

1/x + 1/y = 1/4

Since we know that x = 3y, we can substitute this into the equation and solve for y:

1/3y + 1/y = 1/4

Combining the fractions on the left side, we get:

4/3y = 1/4

Multiplying both sides by 12y to clear the fractions, we have:

16 = 3y

Dividing both sides by 3, we find that y = 16/3 = 5.33

Therefore, it would take Bailey approximately 5.33 days to paint the house alone. And since x = 3y, it would take Andrew approximately 3(5.33) = 15.99 or 16 days to paint the house alone.