Work

Question 1

Rate Time Work Formula

Answer 1

Rate x Time = Work

(Same as Rate x Time = Distance)

Question 2

4 Types of Work Problems

Answer 2

1. Single worker
2. Combined worker
3. Opposing worker
4. Change in workers

Question 3

Adding Combined Rate

Answer 3

Compute the combined rate of 2 or more objects by adding the individual rates of the objects. If one object can complete a job in x hours and another can complete the same job in y hours, the combined rate of the 2 objects is 1/x + 1/y.

Why? Assume both work for t amount of time together.
→ Total work ÷ t = Combined rate
→ [(1/x)t + (1/y)t] ÷ t = 1/x + 1/y

Question 4

Combined Worker

Answer 4

• When two objects work together, Work₁ + Work₂ = Work_Total
• For problems in which two objects begin a task together but one of the object stops and the other object must finish the job alone, let the work time for the object that stops first be represented by x and 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.
• When working together for x amount of time, all objects work for the same amount of time (i.e., x)

Question 5

Opposing Worker

Answer 5

When two objects are working against each other, their individual work values must be subtracted from each other: the total task equals the difference between their work values.

Question 6

Change in Workers

Answer 6

When workers working at the same constant rate are added or removed from a group, we can determine the new rate of the workers using either of the two following 2 methods:

1. Determining the rate of one worker
2. Proportion method

Question 7

Change in Workers: Proportion Method

Answer 7

People_x / Rate_x = People_y / Rate_y

Set up a matrix (see image)

Question 8

Work: Hard Problem

Answer 8

When Jefferson works alone, he can mow n lawns in x minutes. When Robert works alone, it takes him 20 minutes longer than it takes Jefferson to mow n lawns. If Jefferson and Robert both work together at their own individual constant rates to mow n lawns in t minutes, how many minutes would it take Jefferson to mow n lawns by himself?

1. n = 10
2. The two men work together for 24 minutes

Answer: B. You know how to set up the RTW and solve for x min using statement #2. Then, you actually don’t need the value for n to answer the question!