Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

Step-by-step explanation:

Step 1: Know the key information

Catherine = 15 hours

Dan=30 hours

Time to work together = x

Step 2: Put them as fractions

So: Catherine=1/15

Dan=1/30

Time to work together = 1/x

Therefore, our equation will be: 1/15+1/30=1/x

Step 3: Our lowest common denominator is 30x

Therefore,

30x/15=2x

30x/30=x

30x/x=30

Step 4: put the x we found into a equation

Our equation would be:

2x+x=30 which makes

3x=30 (divide 30 by 3 as 30 is a multiple of 3)

x=10

Therefore, when working together it would take 10 hours