Question

Person A can paint the neighbors house 5 times as fast as Person B. The year A and B worked together, it took them 6 days. how long would it take each to paint the house

Answer 1

You have to think of these problems in terms of how much work is done in a given time
With this in mind we can create this equation.
1/x + 1/5x = 1/6

Answer 2

Can You solve it now?

Answer 3

yes i believe so thanks

Answer 4

i got 36/5

Answer 5

Person A takes x days to paint the house.
Person B takes 5x days to paint the house.

In 1 day, person A does 1/x of the job.
In 1 day, person B does 1/(5x) of the job.
In 1 day, both working together do 1/6 of the job.

\(\dfrac{1}{x} + \dfrac{1}{5x} = \dfrac{1}{6} \)

x is the time the faster person takes to paint the house.
5x is how long the slower person takes.

Answer 6

x = 36/5 = 7.2 days
The faster of the 2 takes 7.2 days to the the complete job.
The slower one takes 5 times as long.
What is 36/5 * 5 ?

Answer 7

36

Answer 8

so
person A would take 36/5 days
and
person B would take 36 days

Answer 9

Right.
Now let's check.

The slow painter needs 36 days working alone.
In 6 days he does 6/36 of the job. That means he does 1/6 of the job in 6 days.

The fast painter needs 7.2 days working alone.
In 6 days, he does 6/7.2 of the job. 6/7.2 = 5/6. He does 5/6 of the job in 6 days.

1/6 of the house (painted by the slow painter) + 5/6 of the house (painted by the fast painter) = 1 entire house painted.

Answer 10

Yes. Answers are 7.2 days and 36 days.