To fulfill an assignment by a given deadline, a team of workers had to produce 54 parts daily. Exceeding the schedule by 6 parts per day, the team not only finished the assignment 1 day earlier, but also produced 18 extra parts. How many days did the team work?

We have been been given that to fulfill an assignment by a given deadline, a team of workers had to produce 54 parts daily. So the number of parts produced in d days will be [tex]54d[/tex].

After exceeding the the schedule by 6 parts per day number of parts produced in will be [tex]54+6=60[/tex] parts per day.

As after exceeding the schedule by 6 parts per day, team finished the assignment 1 day earlier, so number of days will be d-1.

So after exceeding the schedule the total number of parts produced in d days will be [tex]60(d-1)=60d-60[/tex]

We are also told that exceeding the schedule by 6 parts per day, the team produced 18 extra parts.

We can represent this information in an equation as:

[tex]54d+18=60d-60[/tex]

Let us solve for d by combining like terms.

[tex]54d-60d+18-18=60d-60d-60-18[/tex]

[tex]54d-60d=-60-18[/tex]

[tex]-6d=-78[/tex]

Upon dividing both sides of our equation by -6 we will get,

[tex]\frac{-6d}{-6}=\frac{-78}{-6}[/tex]

[tex]d=13[/tex]

Therefore, before exceeding the schedule team will finish the assignment in 13 days.

As team finished the assignment 1 day earlier, so number of days taken by team will be:

[tex]d-1=13-1[/tex]

[tex]d=12[/tex]

Therefore, after exceeding the schedule by 6 parts per day, the team took 12 days to complete the assignment.