Multiple choice

A takes $5$ days less than $B$ to complete the work. Both complete the work in $6$ days. In how many days $A$ complete the work?

  1. $10$
  2. $15$
  3. $20$
  4. $30$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B take x days, A takes x-5. 1/(x-5) + 1/x = 1/6. (x + x - 5) / (x^2 - 5x) = 1/6. 12x - 30 = x^2 - 5x. x^2 - 17x + 30 = 0. (x-15)(x-2) = 0. x=15. A takes 15-5 = 10 days.

AI explanation

Let A take x days to complete the work alone, so B takes x + 5 days. Their combined one-day work is 1/x + 1/(x + 5) = 1/6. Multiplying by the least common multiple of 6x(x + 5) gives the quadratic equation 6(x + 5) + 6x = x(x + 5), which simplifies to x^2 - 7x - 30 = 0. Factoring this gives (x - 10)(x + 3) = 0, and since time must be positive, x is 10. The correct result is 10 days.

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