It would take them [tex]3\frac{3}{7}[/tex] hours to paint the house together.
Step-by-step explanation:
Time taken by Cassandra = 6 hours
Time taken by her assistant = 8 hours
Let,
x be the time taken by both.
Cassandra part in painting house = 1/6 hours
Her assistant's part = 1/8 hours
[tex]\frac{1}{6}+\frac{1}{8}=\frac{1}{x}\\[/tex]
Taking LCM
[tex]\frac{4+3}{24}=\frac{1}{x}\\\frac{7}{24}=\frac{1}{x}[/tex]
[tex]x=\frac{24}{7}\\x=3\frac{3}{7}[/tex]
It would take them [tex]3\frac{3}{7}[/tex] hours to paint the house together.
Keywords: addition, LCM
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