work gets finished in first 5 days after they start working right?

Question

Three contractors, X, Y, and Z, can complete a construction project in 12, 15, and 20 days, respectively. If they all start working together, but after 6 days, contractor Z leaves the project, and contractor Y leaves after 8 more days, how many more days will it take for contractor X to complete the remaining work?

Simran Mehta · Accepted Answer

Calculate the work rates for each contractor:
Contractor X: rate_X = 1/12 of the work per dayContractor Y: rate_Y = 1/15 of the work per dayContractor Z: rate_Z = 1/20 of the work per dayCalculate the total work done in the first 6 days by all three:
Total rate when all three work together: (1/12) + (1/15) + (1/20)Total rate: 1/12 + 1/15 + 1/20 = (5/60) + (4/60) + (3/60) = 12/60 = 1/5Work done in 6 days: 6 * (1/5) = 6/5 = 1.2Calculate the remaining work after 6 days:
Total work to be done: 1Work done in 6 days: 1.2Remaining work: 1 - 1.2 = -0.2The correct steps:
Calculate the work done by all three in the first 6 days:
Total rate of all three contractors: 1/12 + 1/15 + 1/20 = 1/5 per dayWork done in 6 days: 6 * 1/5 = 6/5 = 1.2 (work units)Calculate the remaining work after the first 6 days:
Total work required: 1 (work unit)Work done in first 6 days: 1.2 (work units)Since 1.2 work units exceed the total work required (1 work unit), the remaining work after 6 days is 0.Since contractors X, Y, and Z completed the project within the first 6 days, no additional work or time is required.Summarized conclusion:
All contractors together completed the project in the first 6 days, making any additional days unnecessary.