Question

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?

Answer 1

Team worked for 12 days.

Explanation:

Let d be the number of days.

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
`54d`.

After exceeding the the schedule by 6 parts per day number of parts produced in will be
`54+6=60` 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
`60(d-1)=60d-60`

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:

`54d+18=60d-60`

Let us solve for d by combining like terms.

`54d-60d+18-18=60d-60d-60-18`

`54d-60d=-60-18`

`-6d=-78`

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

`(-6d)/(-6)=(-78)/(-6)`

`d=13`

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:

`d-1=13-1`

`d=12`

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