Time & Work

Algebra Level 3

A & B can do a piece of work in 18 days; B & c can do it in 24 days; A & C can do it in 36 days. In how many days will it take for B to finish alone?


The answer is 28.8.

Sanket Savale by Sanket Savale , 27, India

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2 solutions

1 B + 1 C − ( 1 A + 1 C ) = 1 24 − 1 36 ; 1 B − 1 A = 1 72 \frac{1}{B} + \frac{1}{C} - (\frac{1}{A} + \frac{1}{C}) = \frac{1}{24} - \frac{1}{36} ; \frac{1}{B} - \frac{1}{A} = \frac{1}{72}

1 B − 1 A + ( 1 B + 1 A ) = 1 72 + 1 18 ; 2 B = 5 72 \frac{1}{B} - \frac{1}{A} + (\frac{1}{B} + \frac{1}{A}) = \frac{1}{72} + \frac{1}{18} ; \frac{2}{B} = \frac{5}{72}

B = 2 × 72 5 = 28.8 B = 2 \times \frac{72}{5} = \boxed{28.8}

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Christian Daang
Oct 21, 2014

By Given Problem,

1/A + 1/B = 1/18 (i)

1/A + 1/C = 1/36 (ii)

1/B + 1/C = 1/24 (iii)

Subtract: (i) and (ii)

Giving us:

1/B - 1/C = 1/36 (iv)

equate (iii) and (iv)

1/B + 1/C = 1/24

1/B - 1/C = 1/36

Adding them,

2/B = 5/72

B = 144/5 = 28.8

Final Answer: 28.8 Days.. :D

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