Multiple choice

During a community project, Alice and Bob were assigned to paint a mural. Alice can paint 1 3 of the mural in 6 days, and Bob can paint 1 4 of the same mural in 5 days. Quantity A: Number of days it would take for both to finish painting the mural, working together Quantity B: 10 days

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alice paints 1/3 of the mural in 6 days, so she paints 1/18 per day. Bob paints 1/4 in 5 days, so he paints 1/20 per day. Together, they paint (1/18 + 1/20) = (10/180 + 9/180) = 19/180 per day. The time taken is 180/19 days, which is approximately 9.47 days. Since 9.47 < 10, Quantity B is greater.

AI explanation

Alice finishes one-third of the mural in 6 days, so she can complete the entire mural in 18 days, giving a work rate of 1/18 per day. Bob finishes one-fourth of the mural in 5 days, meaning he can complete the entire mural in 20 days, yielding a work rate of 1/20 per day. Working together, their combined rate is 1/18 + 1/20 = 19/180 of the mural per day. Therefore, the time taken by both to finish the mural together is 180/19 days, which is approximately 9.47 days. Since 9.47 days is less than 10 days, Quantity B is greater.

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