Multiple choice

$A$ can cultivate $\displaystyle\frac{2}{5}$ of a land in 6 days and $B$ can cultivate $\displaystyle\frac{1}{3}$ of the same land in 10 days. Working together, $A$ and $B$ can cultivate $\displaystyle\frac{4}{5}$ of the land in:

  1. 4 days

  2. 5 days

  3. 8 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A cultivates 2/5 of the land in 6 days, so A's rate is (2/5)/6 = 1/15 land per day. B cultivates 1/3 of the land in 10 days, so B's rate is (1/3)/10 = 1/30 land per day. Together, their rate is 1/15 + 1/30 = 3/30 = 1/10 land per day; to cultivate 4/5 of the land, they need (4/5) / (1/10) = 8 days.

AI explanation

Using the work rate method, A completes (2/5) of the land in 6 days, so A's 1 day work is 2/5 divided by 6, which equals 1/15. B completes (1/3) of the land in 10 days, so B's 1 day work is 1/30. Working together, their combined 1 day work is 1/15 + 1/30 = 1/10. Therefore, working together, A and B can cultivate 4/5 of the land in (4/5) divided by (1/10) days, which results in 8 days.

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