SAT Help Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job? How do you solve this?

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Well, their speeds are ([latex]V_1[/latex] is Jack's speed, and [latex]V_2[/latex] is Richard's. [latex]V_1 = \frac{1}{5} houses/day \\ V_2 = \frac{1}{7} houses/day \\ V = V_1 + V_2 = \frac{1}{5}+\frac{1}{7} = \frac{7+5}{35} = \frac{12}{35}[/latex] They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate [latex]\frac{35}{12}[/latex] which is very close to 3 (a bit below)

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