Problema Solution
A and B began a certain job on monday and the work was to be completed on tuesday. On monday, A worked for 10 hours and B worked for 8 hours and one-half of the job was done. On tuesday, A had to stop working after only 5 hours, and B had to work a total of 12 hours to complete a job. How long would it have taken each person to do the whole job?
Answer provided by our tutors
We will use the general equation d=rt (where d=job=rate*time). Since A and B are working together to get 1 job done, we can write:
Job=(rate A)(Time A)+(rate B)(Time B)
From the question, we know:
For Monday:
TimeA= 10
TimeB= 8
Job=1/2
For Tuesday:
TimeA=5
TimeB=12
Job=1/2
Therefore, we can write:
1/2=10A+8B
1/2=5A+12B
Using Algebrator to solve for A and B, we get:
A=1/40 job/hour
B=1/32 job/hour
These are the rates of each A and B. Therefore, it would take A 40 hours to finish the whole job and it would have taken B 32 hours.