Multiple choice

A and B can complete work together in 5 days. If A works at twice his speed and B at half of his speed this works can be finished in 4 days. How many days would it take for A alone to complete the job ?

  1. $10.0$
  2. $12.0$
  3. $15.0$
  4. $18.0$
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A Correct answer
Explanation

Let the daily work rates of A and B be a and b, respectively. We have the system of equations a + b = 1/5 and 2a + b/2 = 1/4. Solving this system gives a = 1/10, meaning A alone can complete the work in 10 days.

AI explanation

Using the formula for work rates, 1/A plus 1/B equals 1/5. If A works at twice his speed and B at half his speed, then 2/A plus 1/(2B) equals 1/4. Multiplying the second equation by 2 gives 4/A plus 1/B equals 1/2. Subtracting the first equation gives 3/A equals 3/10, so A equals 10. A alone would take 10 days.

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