Work Problems

Question 1

T/F: similar to rate problems, work problems use the formula rate*time=work?

Answer 1

True

Question 2

for two objects working together: work1+work2 = ?

Answer 2

work_total

Question 3

how do represent worker time for a problem where the workers start a job together but one of them stops working before the job is complete?

Answer 3

let the time for the worker who works less time be x, and the time for the worker who works longer be x+t, where t is the unknown difference in time between when the first worker stops and the job is complete

Question 4

how do we handle the case where the time it takes an object to complete a job (or fraction of a job) is unknown?

Answer 4

let the rate contain the job(s) in the numerator and let the denominator be the variable t. ex: object A can complete 1 job in an unknown amount of time; the rate is 1/t

Question 5

how do you figure out the percent of a job done by a certain worker?

Answer 5

first, find the total amount of work done. since w=r*t, find the contribution of each worker as a function of time (ex. worker 1 puts together 1 bookshelf every 4 hours, and worker 2 does 1 every 8 hours, so their work contributions are t/4, and t/8 respectively), then divide the contribution of the individual worker by the total (the t’s will cancel out)

Question 6

how do you calculate two or more workers combined rate?

Answer 6

add them; if worker A can complete one bench in x hours and worker B can complete one bench in y hours, their combined rate is 1/x+1/y

Question 7

how do you handle opposing worker problems, where one worker “dampens” the rate of work of the other worker?

Answer 7

you subtract the rate of the dampening worker to find the “net” work rate

Question 8

how do you figure out how long it will take a subset (or superset) of an original group of workers whose rate you have been given to complete a job? ex: 5 workers working at same constant rate can complete a job together in 6 days, how long would it take 2 of them to complete the job?

Answer 8

first define rate of five workers: (1 job)/(6 days)

single worker method: find the rate of a single worker. since there are 5 workers, divide the groups rate by 5 -> (1/6)/5 = 1/30. then multiply that single rate by two since you want to know how long it takes to of them ->1/15

proportion method: set up a proportion-> (1/6)/(5) = (1/x)/(2) -> 5 people can do 1 job in 6 days, and two people can do one job in x days