Mary can clean a house in two hours, Gina can clean a house in three hours.

How long would it take for Mary and Gina to clean the house together.

Also please explain how you got the answer.

consider how much of the job gets done in one hour.

Mary does 1/2
Gina does 1/3

So, ever hour, 1/2 + 1/3 = 5/6 of the job gets done.

If 5/6 gets done in one hour, the whole job takes 6/5 hours.

1/2 + 1/3 = 1/x

For further discussions, I refer you to

(a) your class text
(b) your teacher
(c) google: algebra work problems

Mary's rate = house/2

Gina's rate = house/3
combined rate = house/2 + house/3
= 5house/6 , (just like 1/2 + 1/3 = 5/6)

time at combined rate = house/(5house/6)
= house(6)/(5house)
= 6/5

notice that "house" canceled, we could have used anything, some would just use 1

To find out how long it would take Mary and Gina to clean the house together, we need to calculate their combined cleaning rate.

Mary can clean a house in 2 hours, so her cleaning rate is 1 house per 2 hours (1/2 house per hour).
Gina can clean a house in 3 hours, so her cleaning rate is 1 house per 3 hours (1/3 house per hour).

To calculate their combined cleaning rate, we add their individual rates together:
Combined rate = Mary's rate + Gina's rate
Combined rate = 1/2 + 1/3

To add these fractions with different denominators, we need to find a common denominator:
Common denominator = 2 * 3 = 6

Now we can rewrite the fractions with the common denominator:
Combined rate = 3/6 + 2/6
Combined rate = 5/6 house per hour

This means that Mary and Gina can clean 5/6 of a house in one hour.

To find out how long it would take them to clean a whole house, we need to calculate the reciprocal of their combined cleaning rate:
Time = 1 / Combined rate
Time = 1 / (5/6)

To divide by a fraction, we multiply by its reciprocal:
Time = 1 * (6/5)
Time = 6/5 hour

Therefore, it would take Mary and Gina together 6/5 or 1.2 hours (1 hour and 12 minutes) to clean the house.