Multiple choice

3 men finish painting a wall in 8 days. Four boys do the same job in 7 days. In how many days will 2 men and 2 boys working together paint two such walls of the same size?

  1. 6 6/13 days

  2. 3 3/13 days

  3. 9 2/5 days

  4. 12 12/13 days

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

3M = 8 days -> 1M = 24 days. 4B = 7 days -> 1B = 28 days. Work rate of 2M + 2B = 2/24 + 2/28 = 1/12 + 1/14 = (7+6)/84 = 13/84. Time for 1 wall = 84/13 days. Time for 2 walls = 168/13 = 12 12/13 days.

AI explanation

The total work is 24 man-days (3 men times 8 days) or 28 boy-days (4 boys times 7 days), making 1 man equal to 28/24 or 7/6 boys. Two men and two boys equal 14/6 boys plus 12/6 boys, totaling 26/6 boys. Painting two walls requires 56 boy-days (28 boy-days times 2 walls). Dividing 56 boy-days by 26/6 boys gives 336/26 days, which simplifies to 12 12/13 days.