Me and Bill said casey can do the job for you in 10 days but give me alex instead of bill and we can get it done in 9 days. i can do better tha that said slex. let me take bill as a partner and we will do the job for you in 8 days. how long will it take each man to do the job alone
It's not clear who is working and who is just talking.
To determine how long it will take each person to do the job alone, we need to assign variables to their individual work rates. Let's say the work rate of Casey is C (in jobs per day), Bill's work rate is B, Alex's work rate is A, and the total work required to complete the job is 1.
According to the given information:
Casey and Bill together can complete the job in 10 days. So, we can write the equation as:
10(C + B) = 1
Casey and Alex together can complete the job in 9 days. Replacing Bill with Alex, the equation becomes:
9(C + A) = 1
Now, Alex wants to work with Bill. Together, they claim they can complete the job in 8 days.
8(A + B) = 1
Now, we have three equations with three unknowns. We can use these equations to find the values of C, B, and A, which will give us the time taken by each person to complete the job alone.
Let's solve these equations using a method called substitution:
From the first equation, we can express C in terms of B:
C = (1 - B) / 10
Substituting C in the second equation:
(9/10 - 9B/10 + A) = 1 => A = 9B/10 + 1/10
Substituting A in the third equation:
8((9B/10 + 1/10) + B) = 1
Simplifying this equation will give us the value of B.
Once we have the value of B, we can substitute it back into the earlier equations to find C and A.
After finding the values of C, B, and A, we can determine the time it takes for each person to complete the job alone by using the formula:
Time (in days) = 1 / (work rate)
Plug in the respective work rates to find the time taken by each person.