Calculating the days............!

Algebra Level 3

'A' takes 6 days less than the time taken by 'B' to finish a piece of work. If both 'A' and 'B' together can finish it in 4 days, find the time taken by 'B' to finish the work.


The answer is 12.

Tushar Malik by Tushar Malik , 20, India

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2 solutions

George Chen
Aug 3, 2014

set the whole piece of work is 1 and A's time to finish is x. A's rate of working is 1/x, B's rate is 1/(x+6), and the sum of their rates is 1/4, so we have equation: 1/x + 1/(x+6) = 1/4, x= -4 or 6, we take 6, that's A's time, B's time is 12. Solved.

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Christian Daang
Oct 21, 2014

By using the shortcut Product/sum ,

Let x-6 the time A finish the work and x the time b finish the work.

then:

(x-6)(x)/(2x-6) = 4

x^2 - 6x = 8x - 24

x^2 - 14x + 24 = 0

(x - 12)(x-2) = 0

x = {12,2}

Reject x = 2 since it will give us negative time when subtracted by 6.

Therefore, x= the time B finish the work = 12 days.

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