Moe and Curly have been hired to paint the interior of a school during summer break. Moe can paint the entire school in 70 hours by himself. Working together it takes Moe and Curly 40 hours to paint the entire school. Write and solve an equation to determine how long it would take Curly to paint the interior of the school by himself.

Question

05-02-2018
Mathematics

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Moe and Curly have been hired to paint the interior of a school during summer break. Moe can paint the entire school in 70 hours by himself. Working together it takes Moe and Curly 40 hours to paint the entire school. Write and solve an equation to determine how long it would take Curly to paint the interior of the school by himself.

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CastleRook CastleRook · Answer 1 · 2018-02-14T08:28:21+01:00

Time taken for Moe to paint the entire school 70 hours
Time taken for Moe and Curly to paint the entire school is 40 hours
Let the time taken for Curly to paint the entire school be x.
Fraction of work done by Moe in one hour will be 1/70
Fraction of work done by Curly in an hour will be 1/x
Fraction of work done by both in an hour will be 1/40
Hence the total fraction completed by both can be expressed in the equation:
[tex] \frac{1}{40}=\frac{1}{x}+ \frac{1}{70} [/tex]
solving for x we get:
[tex] \frac{1}{40}-\frac{1}{70}= \frac{1}{x} [/tex]
[tex] \frac{3}{280}= \frac{1}{x}[/tex]
hence x will be:
[tex] x=\frac{280}{3} hours [/tex]