Multiple choice

John and Emma are working on a landscaping project for their community park. John can complete 50% of the project in 10 days, while Emma can finish 75% of the project in 15 days. They both work together for 8 days before taking a break. Sarah, a skilled landscaper, then completes the remaining work in 5 days. The community project committee wants to know in how many days it would take John, Emma, and Sarah to collectively finish 35% of similar project if they worked together from the start?

  1. 1.5 days

  2. 2.5 days

  3. 3 days

  4. 4.5 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John rate: 0.5/10 = 0.05/day. Emma rate: 0.75/15 = 0.05/day. Combined rate = 0.1/day. In 8 days, they finish 0.8 of the project. Remaining = 0.2. Sarah does 0.2 in 5 days, so Sarah rate = 0.04/day. Combined rate of all three = 0.05 + 0.05 + 0.04 = 0.14/day. Time to finish 0.35 of the project = 0.35 / 0.14 = 2.5 days.

AI explanation

To find their individual rates, John completes 50% of the project in 10 days, meaning his daily rate is 0.05 (5% or 1/20 of the project). Emma completes 75% in 15 days, so her daily rate is 0.05 (5% or 1/20 of the project). Together, their combined rate is 0.1 (10% or 1/10) per day, meaning in 8 days they complete 0.8 (80%) of the project. This leaves 0.2 (20%) of the project for Sarah to complete in 5 days, making her daily rate 0.04 (4% or 1/25) of the project. Using the additive work method, their combined three-person rate is 0.05 + 0.05 + 0.04 = 0.14 (14%) per day. To complete 35% (0.35) of a similar project, we divide 0.35 by 0.14, which yields 2.5 days.

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