Question

Rachael can paint a room in 9 hours. Kelsey can paint same room in 15 hours. How long if they paint it together.

Answer 1

6 hours

Explanation:

because if they work together it will be 9 hours slower than Kelsey's time alone.

not sure if correct

Answer 2

Rachael and Kelsey when work together will paint the room in 5.625 hours.

Solution:

Given that

Rachael can paint a room in 9 hours.

Kelsey can paint same room in 15 hours.

Need to calculate number of hours to paint same room when both work together

Let say complete work of painting room be represented by w

Paint Work done by Rachael in 9 hours is complete work = w

So Paint Work done by Rachael in 1 hour =
`(w)/(9)`

Paint Work done by Kelsey in 15 hours is complete work = w

So Paint Work done by Kelsey in 1 hour =
`(w)/(15)`

Paint work done by Rachael and Kelsey together in 1 hour is given as:

`=(w)/(9)+(w)/(15)=(5 w+3 w)/(45)=(8 w)/(45)`

So number of hours required to complete work when both work together is given as:

`=\frac{\text { Total work }}{\text { work done by them togther in } 1 \text { hour }}=(w)/(\left((8 w)/(45)\right))=5.625 \text { hours }`

Hence Rachael and Kelsey when work together will paint the room in 5.625 hours.