There are three kinds of machines A, B, and C for doing a certain work.
The work will be completed exactly in 35 days if I use one A and one B simultaneously.
The same work will be exactly completed in 20 days if I use one A and three B simultaneously.
Moreover, it will be exactly completed in 14 days, if I use two A and five C simultaneously.
Find the number of days which I can complete the work using one A, one B, and one C simultaneously.
The work will be completed exactly in 35 days if I use one A and one B simultaneously.
The same work will be exactly completed in 20 days if I use one A and three B simultaneously.
Moreover, it will be exactly completed in 14 days, if I use two A and five C simultaneously.
Find the number of days which I can complete the work using one A, one B, and one C simultaneously.
Answer
28 days
Solution
The overall workload is set to 140 of the least common multiple of 35, 20, and 14.
The sum of daily workload of one A and one B is 140 / 35 = 4.
The sum of daily workload of one A and three B is 140 / 20 = 7.
Because 7 - 4 = 3 expresses the daily workload of two B, the daily workload of one B is 3 / 2 = 1.5.
The daily workload of one A is 4 - 1.5 = 2.5.
The sum of daily workload of two A and five C is 140 / 14 = 10.
The daily workload of one C is (10 - 2.5 × 2) / 5 =1.
Thus, the sum of daily workload of one A , one B and one C is 2.5 + 1.5 + 1 = 5.
Therefore, it takes 140 / 5 = 28 days.
The sum of daily workload of one A and one B is 140 / 35 = 4.
The sum of daily workload of one A and three B is 140 / 20 = 7.
Because 7 - 4 = 3 expresses the daily workload of two B, the daily workload of one B is 3 / 2 = 1.5.
The daily workload of one A is 4 - 1.5 = 2.5.
The sum of daily workload of two A and five C is 140 / 14 = 10.
The daily workload of one C is (10 - 2.5 × 2) / 5 =1.
Thus, the sum of daily workload of one A , one B and one C is 2.5 + 1.5 + 1 = 5.
Therefore, it takes 140 / 5 = 28 days.
