Problema Solution
A computer encoder A can finish a job in as many as many days as encoder B. Encoder C can finish the same job in 2 days less than encoder B. Together the three encoders worked for 2 days after which encoder A and B got sick and were forced to stop working leaving encoder C alone to finish the job in three more days. Find the rate of each encoder.
Answer provided by our tutors
Let a, b, and c stand for the rates of Encoder A, B, and C respectively. From the question, we can write:
a=b
1=c((1/b)-2)
1=2(a+b+c)+3c
We use the general equation d=rt (where d is number of jobs, r is rate, and t is time in days). Rates are in jobs per day. The second equation was formed from:
1=bt (formula for 1 job for B)
1=c(t-2) (formula for the same job as B did, but for encoder C)
't' is the same in both equations. substituting, we get:
1=c((1/b)-2)
Now we will solve for a, b, and c in the below equations.
a=b
1=c((1/b)-2)
1=2(a+b+c)+3c
We get:
a=.09788 job/day
b=.09788 job/day
c=.1217 job/day