Does anyone know the formula or how to format the following word problem?

Painter X can paint a house in 4 hours. Painter Y can paint the same house in 6 hours. How long will it take for both painters to paint the same house together?

I was told the answer was 2 hours and 24 minutes but don't know how to put it in a formula that can be worked.

Thanks for the assistance.

Dave

\frac{1}{4}+\frac{1}{6}=\frac{1}{t}

Solve for t and convert from decimal to hours and minutes.

You can also do this:

\frac{t}{4}+\frac{t}{6}=1

Gives same answer.

For the second method, we are figuring up the time to paint 1/4th the house and 1/6th the house. Together, 1 whole house is painted.

Yup, one painter alone would take more time than when both painters work together.

I hahve almost the same as galactus, but equal to 1/T ,i.e
1/4 + 1/6=1/T
5/12=1/T you switch both fractions and you have T=12/5 equal to 2 2/5 (2/5 of 60 minutes is equal 24 minutes)
Final answer: 2 hrs and 24 minutes