your question is missing the given conditions, here is the complete question;
Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?
(1) The average time A and B can complete the task working alone is 12.5 days.
(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task
Answer:
Machine A, working alone, can complete the task in 15 days.
Explanation:
As the average is given as 12.5 so,
A+B=2*12.5
A+ B=25
second condition says machine A takes 5 more days to complete the task alone than B so
A=B+5........Eq1
Now from the question statement we can get that
1/A+1/B=1/6, where A is time needed for A to do the task alone and B is the time needed for B to complete the task alone
thus, simplyfing above equation we get as
AB/A+B=6; \\ putting A+B=25 we get
AB/25=6
AB=6*25
AB=150; \\ putting Eq1 we get
(B+5)B=150
B^2+5B-150=0
simplifying the quadratic equation above we get B=10
putting B=10 in Eq1, we get
A+10=25
A=15
Thus, Machine A, working alone, can complete the task in 15 days.
