Patrick can paint a house by himself in t+4 hours. Karen can paint the same house by herself in t+9 hours. If they work together

Question

2 years ago

15

, they can paint the house in t hours. How much time will it take for Patrick to paint the house by himself?

1 answer:

vladimir2022 [97] · Answer 1 · 2023-08-10T03:24:00+03:00

Patrick will be able to paint the home on his own after a ten-hour effort.

This is further explained below.

<h3>How much time will it take for Patrick to paint the house by himself?</h3>

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.