A and B can complete a piece of work together in 5 days. If A works at bwice his speed and B at half of his speed, the work can be finished in 4 days. How many days would it take for A alone to complete the work?
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A can do work in X number of days
B can do work in Y number of days
Per day they can do: 1/X + 1/Y together.
in 5 days : 5/X + 5/Y. = total Work amount
2 * 1/X + 1/2 * 1/B = work per day after they change their speeds
4 * (2/X + 1/2*B) = total work = 5/X + 5/Y
1/X * 3 = 1/Y * 3 => X = Y
Hence the total work = 1/X * 5 + 1/X * 5 = 10 * 1/X
number of days for A to complete alone: (10/X) / (1/X) = 10 days
B can do work in Y number of days
Per day they can do: 1/X + 1/Y together.
in 5 days : 5/X + 5/Y. = total Work amount
2 * 1/X + 1/2 * 1/B = work per day after they change their speeds
4 * (2/X + 1/2*B) = total work = 5/X + 5/Y
1/X * 3 = 1/Y * 3 => X = Y
Hence the total work = 1/X * 5 + 1/X * 5 = 10 * 1/X
number of days for A to complete alone: (10/X) / (1/X) = 10 days
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