SOLUTION: jessica and cynthia work in a pet shop. it takes jessica 6 hours to groom all the pets but cynthia needs 8 hours to groom them. if jessica starts to groom 1 hour before cynthia joi

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Question 978681: jessica and cynthia work in a pet shop. it takes jessica 6 hours to groom all the pets but cynthia needs 8 hours to groom them. if jessica starts to groom 1 hour before cynthia joins, how long will it take them to finish?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
jessica and cynthia work in a pet shop.
it takes jessica 6 hours to groom all the pets but cynthia needs 8 hours to groom them.
if jessica starts to groom 1 hour before cynthia joins, how long will it take them to finish?
:
let t = time it takes them to finish (C's working time)
then
t+1 = J's working time
let 1 = completed job (all pets groomed)
:
A shared work equation, each does a fraction of the job, the two fractions add up to 1
%28%28t%2B1%29%29%2F6 + t%2F8 = 1
Multiply by the least common multiple of 6 and 8, 24. cancel the denominators
4(t+1) + 3t = 24
4t + 4 + 3t = 24
4t + 3t = 24 - 4
7t = 20
t = 20/7
t = 26%2F7 hrs, which is: 2 + 6%2F7*60 = 2 hrs 51.43 min to finish the job