Multiple choice

One morning, Aditi began designing a project at 8 AM, and Bhavna joined her 3 hours later. They worked together and completed the project at 8 PM the same day. Had they both started working together at 8 AM, the project would have been finished 1.5 hours earlier. Working alone, the time Aditi would take to complete the entire project, in hours, is:

  1. 15

  2. 19

  3. 21

  4. 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B be the rates of Aditi and Bhavna. Total time from 8 AM to 8 PM is 12 hours. Aditi works 12 hours, Bhavna works 9 hours. 12A + 9B = 1 (project). If they started together, they finish in 10.5 hours: 10.5(A+B) = 1. Solving the system: 12A + 9B = 1 and 10.5A + 10.5B = 1. From second, B = 1/10.5 - A. Substitute into first: 12A + 9(1/10.5 - A) = 1 => 3A = 1 - 9/10.5 = 1.5/10.5 = 1/7. A = 1/21. Aditi takes 21 hours.

AI explanation

Let Aditi's hourly work rate be A and Bhavna's be B. Working from 8 AM to 8 PM takes 12 hours, so Aditi works for 12 hours and Bhavna works for 9 hours, giving the equation 12A + 9B = 1. If they started together, they would finish in 10.5 hours, giving 10.5A + 10.5B = 1. Multiplying the second equation by 6 and dividing by 7 yields 9A + 9B = 6/7. Subtracting this from the first equation gives 3A = 1/7, so A = 1/21. This means Aditi alone takes 21 hours to complete the project.

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