Multiple choice

Kim and Dominic can paint their apartment in $2$ days. Working alone, Kim can complete the job in $3$ days less than Dominic, working alone. How long would it take Kim to complete the painting, working alone?

  1. $3$ days
  2. $5$ days
  3. $4$ days

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Dominic take x days. Kim takes x-3 days. 1/x + 1/(x-3) = 1/2. 2(x-3 + x) = x(x-3). 4x - 6 = x^2 - 3x. x^2 - 7x + 6 = 0. (x-6)(x-1) = 0. x=6. Kim takes 6-3 = 3 days.

AI explanation

Let Dominic take x days, so Kim takes (x - 3) days. Using the combined work formula, 2 times x plus 2 times (x - 3) equals x times (x - 3), which simplifies to x squared minus 7x plus 6 equals zero. Factoring gives x equal to 6 or 1, but x equal to 1 is invalid because x minus 3 would be negative. Dominic takes 6 days and Kim takes 6 minus 3 days, resulting in 3 days.

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