Multiple choice

D, E, and F can complete a project in 30 days, 24 days, and 20 days respectively. If D and F work together for y days and E completes the remaining work alone in 4y days, then find the value of 2y.

  1. 8

  2. 10

  3. 12

  4. 6

  5. 4
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A Correct answer
Explanation

Rates are D=1/30, E=1/24, F=1/20. Work done by D and F in y days is y(1/30 + 1/20) = y(5/60) = y/12. Remaining work is 1 - y/12. E completes this in 4y days: 4y(1/24) = 1 - y/12. So y/6 = 1 - y/12, which means 3y/12 = 1, so y = 4. Thus 2y = 8.

AI explanation

Let the total work be the least common multiple of 30, 24, and 20, which is 120 units. D's efficiency is 120 divided by 30, which is 4 units per day; E's efficiency is 120 divided by 24, which is 5 units per day; and F's efficiency is 120 divided by 20, which is 6 units per day. D and F work together for y days, completing (4 + 6)y = 10y units of work. E works alone for 4y days, completing 5 x 4y = 20y units of work. The total work is 10y + 20y = 30y units, which must equal the 120 units of total work; solving gives y = 4. The value of 2y is 2 x 4 = 8. The result is 8.

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