It takes emily eight hours to paint her house. mike can paint the same area in nine hours. find how long it would take them if they worked together.

7.58 hours

15.34 hours

3.56 hours

4.24 hours

it would take them 4.24 hours

Step-by-step explanation:

It takes Emily eight hours to paint her house. Her unit rate of working in terms of hours would be 1/8

Mike can paint the same area in nine hours. Mike's unit rate of working in terms of hours is 1/9

If both of them can work together,Then, the work would take lesser time because they would be working together at their own unit rates. This means that the rates are additive. Their combined rates would be 1/8 + 1/9

Let t be the time it takes them to finish the work together. This means that their unit rate of working together will be 1/t. Therefore,

1/8 + 1/9 = 1/t

17/72 = 1/t

17t = 72

t = 72/17

t = 4.24

8/9n - 1 1/3

BTW * MEANS TIMES

Step-by-step explanation:

Given that:   4/9(2n - 3) [1]

The distributive property says that:

a * (b + c) = a * b + a* c

Apply the distributive property in equation [1] we get;

4/9 *  2n + 4/9 * (-3)

Simplify:

8/9n - 4/3

We can write 4/3  in mixed fraction as:

4/3 = 1 1/3

then;

8/9n - 1 1/3

Therefore, the expression which is equivalent to 4/9(2n - 3)  is, 8/9n - 1 1/3