Did I find the time of each worker correctly in this algebra question?

Check your units or measure.

OOPS lol

Haha thanks…I wish I could delete this now.

my answer deleted by me

Your solution was nicely written with its own internal logic but as you might suspect completely wrong. Remember that the two of them working together finish the house in fewer hours than either alone, so you can’t just add hours. It’s tricky that way. Time is the reciprocal of rate. Here’s what I mean…

Let T = Ty’s rate of building, in houses per hour—presumably a small fraction)
and E = Ey’s rate of building (likewise)

Then the stated problem translates as follows:
1/T + 1/E = 24 (hours per house)
1/T = 1/E – 6 (hours per house)

This leads to a simple solution…
Good luck working it out!

Oops, I goofed & my answer was also completely wrong. My second equation is valid, but with the first equation I fell into the same trap you did, adding hours together. The quantity that is additive is the rate of painting in units of houses/hr. T+E represents their combined effort.

The correct first equation is therefore
1 / (T+E) = 24 (hours per house)

I solved for T in terms of E (2nd eq) and substituted into the above to yield a quadratic, with irrational roots, one positive and one negative. The positive number makes perfect sense, however, and satisfies the conditions of the problem.

Turned out to be more difficult than anticipated.

OK, a more minor goof this time—made a mistake in deriving the quadratic & the coefficients were off a little. Both roots are positive & irrational but only one makes sense. Without revealing the exact answer, I can tell you that Ty alone takes almost 2 days to paint a house and Ey alone takes over 2 days.