Multiple choice

A can do a piece of work in $7$ days of $9$ hr each and B can do it in $6$ days of $7$ hr each. How long will they take to do it working together $\displaystyle \frac{42}{5}$ hr a day?

  1. $3$ days
  2. $4$ days
  3. $4.5$ days

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

A's total work time = 7 * 9 = 63 hours. B's total work time = 6 * 7 = 42 hours. Combined rate = 1/63 + 1/42 = (2+3)/126 = 5/126 work per hour. Working 42/5 hours a day, daily work = (5/126) * (42/5) = 1/3 of the work per day. Total days = 3.

AI explanation

A requires 63 hours to finish the work and B requires 42 hours, so their hourly rates are 1/63 and 1/42 of the work respectively. Working together, their combined hourly rate is 1/63 + 1/42 = 5/126 of the work per hour. Since they work 42/5 hours a day, their daily output is (5/126) * (42/5) = 1/3 of the work. Therefore, they finish the entire work in 3 days.

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