Multiple choice

$A$ and $B$ are working together to complete the work in $6$ days. $A$ working alone, can complete the job in $5$ days less than $B$, working alone. How long would it take $A$ to complete the work alone?

  1. $10$ days
  2. $9$ days
  3. $8$ days
  4. $7$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A take x days and B take x+5 days. Their combined rate is 1/x + 1/(x+5) = 1/6. Solving x^2 + 5x = 6(2x + 5) leads to x^2 - 7x - 30 = 0, which factors to (x-10)(x+3) = 0. Thus, A takes 10 days.

AI explanation

Let B take x days, so A takes (x - 5) days. Using the combined work formula, 6 times x plus 6 times (x - 5) equals x times (x - 5), which simplifies to x squared minus 17x plus 30 equals zero. Factoring gives x equal to 15 or 2, but x equal to 2 is invalid because x minus 5 would be negative. B takes 15 days and A takes 15 minus 5 days, resulting in 10 days.

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