Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick

Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick. Find the time taken by Musyoka to complete the cultivation.

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Let Musyoka take x days

In 1 day Mutua cultivates $\frac{1}{15}$

In 1 day Musyoka cultivates $\frac{1}{x}$

In 1 day both had done

$\frac{1}{6}$ x 4 = $\frac{2}{3}$

Fraction of work remaining is

1 - $\frac{2}{3}$ = $\frac{1}{3}$

To complete the work

$\frac{1}{15}$ + $\frac{1}{x}$ = $\frac{1}{6}$; $\frac{1}{x}$ = $\frac{1}{6}$ - $\frac{1}{15}$; $\frac{1}{x}$ = $\frac{1}{10}$

x = 10 days: Musyoka alone would take 10 days to complete the work.

To complete the remaining $\frac{1}{3}$

Musyoka would take

$\frac{1}{10}x$ = $\frac{1}{3}$; x = $\frac{10}{3}$ = 3$\frac{1}{3}$ days

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johnmulu answered the question on March 6, 2017 at 06:32

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