Problema Solution
It would take Tom 10 hours to paint the fence around his backyard by himself. After Tom has been painting for 2 hours, Jerry comes to help him and together they finish painting the fence in 3 more hours. How many hours would it have taken Jerry to paint the whole fence by himself?
Answer provided by our tutors
Tom can complete 1 job/10 hr = 0.10 job/hr. After 2 hours, Tom has completed (2 hr)(0.10 job/hr) = 0.20 job. So that much of the work has been done at the time Jerry joins the fun. That means they need to complete 0.80 job working together. Since Jerry's work rate is unknown, we can set up this equation to find out what it is:
(0.10 job/hr + x job/hr) 3 hrs = 0.80 jobs.
Now all we have to do is solve for x, the fractional part of a job per hour that Jerry can complete working alone:
(0.30 job + 3 hrs (x job/hr) = 0.80 job
3 hrs (x jobs/hr) = 0.80 job - 0.30 job
3 hr (x jobs/hr) = 0.50 job
x job/hr = (½ job)/(3 hr)
x job/hr = [½/(3)] job)/hr
x job/hr = 1 job/6 hr.
It would take Jerry 6 hours to paint the whole fence working alone.