suppose one painter can paint the entire house in twelve hours, and the second p...

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August 2022 1 16 Report

suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similarly-sized house. How long would it take the two painters together to paint the house? Checking is needed right now :-)

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Keltan

Verified answer

Given:

Painter A= 12 hours (Means he can do $\frac{1}{12}$ job a day)
Painter B= 8 hours (Means he can do $\frac{1}{8}$ job a day)
Painter A + Painter B= 1 job (Rate together is equal to $\frac{1}{x}$ )

Solution:

$\frac{1}{12} + \frac{1}{8} = \frac{1}{x}$
Multiply then by 24x to simplify the equation
2x+3x=24
5x=24
x= $\frac{24}{5}$

Therefore, they can complete the job together in 4 hours and 48 minutes.

Checking:

Substitute the value of x to the original equation:

$\frac{1}{12} + \frac{1}{8} = \frac{1}{x}$
$\frac{1}{8} + \frac{1}{12} = \frac{1}{ \frac{25}{4} }$
$\frac{2}{24} + \frac{3}{24} = \frac{5}{24}$
$\frac{5}{24}= \frac{5}{24}$

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