Painting the fence

Algebra Level 2

How long will it take Marvin and Kalngan together to paint a fence, which Marvin can paint alone in 4 days and Kalngan alone in 2 days?

1 1 3 1 \frac 13 2 1 2 2 \frac 12 3 3 1 1 2 1 \frac 12

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1 solution

Chew-Seong Cheong
Sep 20, 2016

Let the to paint the fence be W W , the rates of painting of Marvin and Kalngan be m m and k k per day respectively. Then m = W 4 m = \dfrac W4 and k = W 2 k = \dfrac W2 . It the number of days for two of them to paint the fence be t t . Then we have:

( m + k ) t = W t = W m + k = W W 4 + W 2 = 1 1 4 + 1 2 = 1 3 4 = 4 3 = 1 1 3 \begin{aligned} (m+k) t & = W \\ \implies t & = \frac W{m+k} = \frac W{\frac W4 + \frac W2} = \frac 1{\frac 14 + \frac 12} = \frac 1{\frac 34} = \frac 43 = \boxed{1\frac 13} \end{aligned}

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