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?

Answer 1

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.