Patrick will be able to paint the home on his own after a ten-hour effort.
This is further explained below.
Generally, the equation for time is mathematically given as
1/(t+4) + 1/(t+9) = 1/t
Therefore
[1/(t+4)] (t+4)(t+9)(t) + [1/(t+9)](t+4)(t+9)(t) = (1/t)(t+4)(t+9)(t)
(t² + 9t) + (t² + 4t) = t² + 13t + 36
Place the equation on the left side of the page and make it equal to 0. Use the additive inverse property as follows:
t² + t² - t² + 9t + 4t - 13t - 36 = 0
2t² - t² + 13t - 13t - 36 = 0
t² - 36 = 0
Calculate the product of the difference of two squares using the formula t2 - 36 = 0.
Both the total and the difference between the two terms constitute the factors.
(t + 6) (t - 6) = 0
t + 6 = 0
t = -6
t - 6 = 0
t = 6
Choose the positive value for time, t = 6 hours.
It will take 10 hours for Patrick to paint the house alone.
Patrick will be able to paint the home on his own after a ten-hour effort.
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