Work Problems

Question 1

What is the basic formula for a work problem?

Answer 1

1/x + 1/y = 1/z, where x and y are the number of days it takes two people to do a job when they work alone, respectively, and z is the number of days they can complete the job when they work together

Question 2

What is the term for when the works of two entities are subtractive, rather than additive?

Answer 2

undoing the job (ex. if one pipe is pouring water into a tank while another empties it out, they are subtractive. If filling the tank is your objective, than the additive pipe is doing the job and the draining pipe is undoing it, and vice versa)

Question 3

If the individual or together times in a work problem are not for the same amount of work, what must be changed about the formula 1/x + 1/y = 1/z?

Answer 3

the numerator isn’t one, but rather a variable that corresponds to the amount of work done.

Question 4

What is the formula for when individual and together times are not for the same amount of work?

Answer 4

p/x + q/y = r/z, where the numerator in each term is the amount of work and the denominator is the time required to complete the work

Question 5

In an inverse proportionality concept with work problems, if we take two ordered pairs (x₁, y₁) and (x₂, y₂) of the variables x and y that follow inverse proportionality relation, what is the output formula?

Answer 5

x₁ * y₁ = x₂ * y₂

Question 6

In a direct proportionality concept with work problems, what three quantities are we given?

Answer 6

number of people (p), amount of work (w), and the time required to complete the work (t)

Question 7

What must you do before you are able to solve a work problem using the direct proportionality concept?

Answer 7

convert it into a two-variable problem

Question 8

What is the new quantity defined in the direct proportionality concept with work problems?

Answer 8

Effort (e)

Question 9

What is the formula for effort?

Answer 9

e = p * t, where p is the number of people put to work and t is the time required for them to complete the work

Question 10

Why does effort and the amount of work have a direct proportionality relation?

Answer 10

Because more effort is required to complete an increased amount of work

Question 11

What is the formula for the direct proportionality concept in work problems?

Answer 11

w1/e1 = w2/e2, where in each term, the numerator defines the amount of work and the denominator is the effort (people * time) required to complete the work