Question

I have been at this for an hour please help

Jason can paint a room in 6 hours. Lorissa can paint a room in only 3 hours.

Which of the following can be used to determine the amount of time it would take for Jason and Lorissa to paint a room together?

1 over 6 plus 1 over 3 equals 1 over x
1 over 6 plus 1 over x equals 1 over 3
1 over x plus 1 over 3 equals 1 over 6
1 over 3 plus 1 over 6 equals x over 9

Answer 1

Jason paints the room in 6 hours.

He does 1/6 of the job in 1 hour.

Lorissa can paint the room in 3 hours.

She does 1/3 of the job in 1 hour.

Together they take x hours to do the job.

In 1 hour, they do 1/x of the job.

In 1 hour they work: 1/6 + 1/3 = 1/x

Answer 2

Answer: First Option is correct.

Explanation:

Since we have given that

Number of hours Jason can paint a room = 6 hours

Number of hours Lorissa can paint a room =3 hours

Work done by Jason per hour is given by

`(1)/(6)`

Work done by Lorissa per hour is given by

`(1)/(3)`

Work done by both of them is given by

`(1)/(6)+(1)/(3)=(1)/(x)\\\\\text{where x denotes number of hours they both need to paint a room}\\\\(1+2)/(6)=(1)/(x)\\\\(3)/(6)=(1)/(x)\\\\(1)/(2)=(1)/(x)\\\\x=2\ hours`

Hence, First Option is correct.