Question

Hayden is a manager at a landscaping company. He has 3 workers to landscape an entire park, Cody, Kaitlyn, and Joseph. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Joseph is new, so no one knows how long it will take him.

Hayden assigns all of them to complete the park together. Explain to Hayden how this project can tell him how long it would take Joseph to complete the project if he worked by himself. Use complete sentences.

Answer 1

A very useful tactic in these sorts of problems is to compute the rate at which each individual works. Sometimes you'll do it as a fraction of the job per hour; other times it will be actual amounts. Then to compute the time for the group, you just divide the quantity of work to be done by the sum of the rates of the workers.

For example:

Bob takes an hour to paint a 50' fence. Joe takes 1/2 an hour to paint a 50' fence. If the two of them have to paint a fence that is 75' long, working together, how long will it take?

Bob does 50'/hr. Joe does 50'/(1/2 hour) = 100'/hr.

Bob + Joe together = 50'/hr + 100'/hr = 150'/hr
Time = work/rate = 75'/(150'/hr) = 1/2 hour.

Answer 2

Oh okay that makes sense! (:

Answer 3

For your problem, you have to work backwards to find the total rate, then subtract off the known rates of Cody and Kaitlyn to find Joseph's rate. But you already figured that out, right?

Answer 4

Yes (: Thank you soooooooooo much!

Answer 5

Great! Be sure to reward my faith in your abilities ;-)

Answer 6

To be perfectly honest I have no idea how to do the whole rewarding thing lol

Answer 7

I have no idea how to work this site

Answer 8

ohhhhhh okay! Thank you (: