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Mathematics

A can do a piece of work in 10 days, B in 18 days, and A, B and C together in 4 days. In what time would C do it alone?

Direct & Inverse Variations

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Answer

A's 1 day work = 110\dfrac{1}{10}

B's 1 day work = 118\dfrac{1}{18}

(A + B + C)'s 1 day work = 14\dfrac{1}{4}

C's 1 day work = 14(110+118)\dfrac{1}{4} - \Big(\dfrac{1}{10} + \dfrac{1}{18}\Big)

= 14(9+590)\dfrac{1}{4} - \Big(\dfrac{9 + 5}{90}\Big)

= 141490\dfrac{1}{4} - \dfrac{14}{90}

= 14745\dfrac{1}{4} - \dfrac{7}{45}

= 4528180\dfrac{45 - 28}{180}

= 17180\dfrac{17}{180}

C can do the work in 18017=101017\dfrac{180}{17} = 10\dfrac{10}{17}

Hence, C can do the work alone in 10101710\dfrac{10}{17} days.

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