Multiple choice

X can do a job in 10 days, Y in 15 days and Z in 18 days. Y and Z begin the work but have to leave after 3 days. How many days will X take to finish the job?

  1. 19/3 days

  2. 57/11 days

  3. 53/12 days

  4. 6.5 days

  5. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X, Y, and Z have rates of 1/10, 1/15, and 1/18 of the job per day. Y and Z work for 3 days, completing 3 * (1/15 + 1/18) = 3 * (6/90 + 5/90) = 3 * (11/90) = 11/30 of the job. X must finish the remaining 19/30 of the job at a rate of 1/10 per day, taking (19/30) / (1/10) = 19/3 days.

AI explanation

Let the total work be 90 units, making the daily work rates of X, Y, and Z equal to 9, 6, and 5 units respectively. Y and Z work together for 3 days, completing 3 times 11 units for a total of 33 units. This leaves 90 minus 33, or 57 units of work remaining for X. Dividing the 57 remaining units by X's daily rate of 9 units gives 57/9 days, which simplifies to 19/3 days.

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