Multiple choice

A can do a piece of work in $6\dfrac {2}{3}$ days and B in $5$ days. They work together for $2$ days and then A leaves B to finish the work alone. How long will B take to finish it?

  1. $\dfrac {3}{4}$ days
  2. $1\dfrac {1}{2}days$
  3. $3\ days$
  4. $7\ days$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1 / (20/3) = 3/20 work/day. B's rate = 1/5 = 4/20 work/day. Combined rate = 7/20 work/day. Work done in 2 days = 2 * (7/20) = 14/20 = 7/10. Remaining work = 3/10. B finishes 3/10 at rate 1/5: (3/10) / (1/5) = 15/10 = 1.5 days.

AI explanation

Converting the mixed fraction, A completes the work in 20/3 days, meaning the daily work rates of A and B are 3/20 and 1/5 respectively. Their combined daily rate is 3/20 plus 1/5, which equals 7/20. Working together for 2 days, they complete 2 times 7/20, leaving 3/10 of the work unfinished. B works alone at a rate of 1/5 per day, so the time to finish the remaining work is 3/10 divided by 1/5, which results in 1.5 days.

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