A and B complete a job if A works two days and B works three days, or if both work 13/5 days. How long would it take each to do the job alone?
1/a + 1/b = 5/13
2/a + 3/b = 1
Now just solve for a and b.
Oobleck, A and B are hypotheticals not numbers
To solve this problem, we can set up equations based on the given information.
Let's assume that A can complete the job alone in x days, and B can complete the job alone in y days.
From the given information, we know that if A works for two days and B works for three days, they can complete the job. This can be expressed as:
1/x + 1/y = 1/2 + 1/3
Similarly, if both A and B work for 13/5 days together, they can also complete the job:
1/x + 1/y = 1/(13/5)
Now, let's simplify these equations.
For the first equation:
1/x + 1/y = 1/2 + 1/3
Multiplying through by 6xy (the least common multiple of 2 and 3), we get:
6y + 6x = 3x + 2y
Rearranging the terms, we have:
4x = 4y
x = y
Now, we can substitute x = y into the second equation:
1/x + 1/y = 1/(13/5)
1/x + 1/x = 5/13
2/x = 5/13
Cross-multiplying, we find:
13x = 10
x = 10/13
So, A can complete the job alone in 10/13 days, and B can complete the job alone in the same amount of time, 10/13 days.
Therefore, it would take A and B each 10/13 days to complete the job individually.