Work Problems

Question 1

Work

Answer 1

Rate*Time

Question 2

The rate at which an object is performing a task or job can be expressed as

Answer 2

Work/Time

Question 3

3 types of rate problems

Answer 3

1) A specific quantity of work completed in a specific amount of time -> 12 cars per month
2) The work as a single job or task completed in a specific amount of time -> 1/4 pool/hour
3) An object completes a fractional amount of work in a specific amount of time -> 3/8 gallon/hour

Question 4

Matrix for solving work problems

Answer 4

Rate * Time = Work

Object Working

Question 5

Single worker problems

Answer 5

Typically, we are asked to either find the rate at which an object works, the time the objects spends working, or the amount of work performed by an object

Question 6

Combined worker problems

Answer 6

When two or more object work together

-> Work (object 1) +Work (object 2)= Work total

Question 7

Two objects work together at the same time

Answer 7

In your table, make the time the same and work from there -> so the time will be x(or same #)

Question 8

Two objects being a job together, but one object stops before completion

Answer 8

1) Let the work time for the object that stops first be represented by x
2) Let the work time for the object that finishes the job alone be represented by (x+y) with y representing the additional time needed to complete the job

Question 9

Two object work together, but one object has an unknown time

Answer 9

1) we can represent the rate at which it can complete the job as 1/t where 1 represents 1 job (work) and the variable t presents the time it takes to do that job
* * If the job being done is more or less than 1 job, we need to account for the numerator
- -> if john can drink 100 sodas in an unknown time, his rate can be expressed as 100/t

Question 10

Percent of a job done and fraction of a job done

Answer 10

• Assume that you both worked the same amount of time
  1) Determine the total work that is performed (since you both work for the same time, let’s let the work time be t)
  2) Work you do/Work total

Question 11

Opposing worker problems

Answer 11

Subtract the work done by one object from the work done by the other object; the work of one retards, reduces the work of the other

Question 12

Rate of one worker is expresses as a multiple of the rate of another worker

Answer 12

• > Tom can drink milk 4 times faster than Joe can drink milk
• > we can let Joe’s rate be some variable r and Tom’s rate be 4r to express the relationship

Question 13

Rate of one worker is slower or faster than the rate of another worker

Answer 13

If object 1 takes x minutes longer than object 2 to complete a job and we let object 2’s time be represented by the variable t minute, object 1’s time would be (t+x) minutes. Then, object 1’s rate would be 1/(t+x) job minutes, and object 2’s rate would be 1/t job/minute

Question 14

One worker can complete a job in some percent (or fraction) greater or less than the time it takes another worker to do the same job

Answer 14

1) If 1 takes x percent fewer minutes than object 2 to complete a job and we let object 2’s work time be t((100-x)/100) minutes.
2) Then, object 1’s rate would be 100/t(100-x) job minutes and object 2’s rate would be 1/t job/minute

Question 15

Change in workers problems

Answer 15

what happens when workers in the group of workers to complete a task when a certain number of workers are added to or removed from a group

• • In these problems we need to
    1) Defining the rate of one worker
    2) The proportion method
• • use proportion to solve these problems