Two teams should work together in the construction of a job

Question

Two teams should work together in the construction of a job and complete the job in 18 days. However, at first, only the Team A worked on the project and left after completing two thirds of the job. Team B finished the rest of the job. The project took 40 days overall. In how many days could each team complete the job separately?

A. Team A - 45 days; Team B - 30 days
B. Team A - 40 days; Team B - 30 days
C. Team A - 40 days; Team B - 35 days
D. Team A - 40 days; Team B - 25 days
E. Team A - 30 days; Team B - 25 days

IanStewart · Accepted Answer

If the two teams were exactly identical, and they divided up the work in the 2/3 and 1/3 split, or any other split at all, and they finished the job in 40 days, then each team alone would take 40 days to do the job. If the teams aren't identical (which they aren't, from the answer choices), one must take longer than 40 days, and one must take less than 40 days. Only answer A is even possible, without even looking at the 18 days information.

That might seem a bit abstract to someone who isn't accustomed to thinking about rates conceptually, so I can explain in reverse. Say you had the teams in answer choice B, so team A takes 40 days alone, and team B takes 30 days alone. If you give all of the work to team A, it will take 40 days, and if you give all of the work to team B, it will take 30 days. If you give some of the work to A, and the rest to B, it will take somewhere between 30 and 40 days, depending on how you divide up the work. So answer B is impossible, because it did not take somewhere between 30 and 40 days when the work was divided between the two teams -- it took 40 days, so one team must take longer than that working alone (unless the two teams both take exactly 40 days).

Kinshook · Answer

Given: Two teams should work together in the construction of a job and complete the job in 18 days. However, at first, only the Team A worked on the project and left after completing two thirds of the job. Team B finished the rest of the job. The project took 40 days overall.

Asked: In how many days could each team complete the job separately?

Let Team A complete the job in x days and Team B complete the job in y days

1/x + 1/y = 1/18

2x/3 + y/3 = 40
2x + y = 120

A. Team A - 45 days; Team B - 30 days: 2x + y = 120: 1/45 + 1/30 = (2+3)/90 = 5/90 = 1/18: Correct
B. Team A - 40 days; Team B - 30 days: 2x + y = 110: Incorrect
C. Team A - 40 days; Team B - 35 days: 2x + y = 115: Incorrect
D. Team A - 40 days; Team B - 25 days: 2x + y = 105: Incorrect
E. Team A - 30 days; Team B - 25 days: 2x + y = 85: Incorrect

IMO A

temporaeum · Answer

Let the rate of team A be 1/a and rate of team B be 1/b (assumed total work as 1)
Total number of days that it took to complete the job was 40
Therefore,
N/a +(40-N)/b = 1 ---------- (we have assumed total word done to be 1)
We are given that N/a = 2/3 => 1/a = 2/3N
This gives us 
2/3 + (40-N)/b = 1
=> (40-N)/b = 1/3 
We are also given that 1/a + 1/b = 1/18
(40-N)(1/18-1/A) = 1/3
This will simplify to, N^2 – 46N + 480 = 0
N = 30 or 16
N/a = 2/90 or 2/48 = 1/45 or 1/24
Thus a = 45 and b = 30 (only option)

Two teams should work together in the construction of a job

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Two teams should work together in the construction of a job

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