SOLUTION: this in rational equations in word problems. Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed

Algebra ->  Rate-of-work-word-problems -> SOLUTION: this in rational equations in word problems. Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed      Log On


   

Question 166983: this in rational equations in word problems.
Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jay can clean the house in 6 hours. After Jay and Jim have both been cleaning for an hour, they are joined by Jen and they completed the cleaning in 2 more hours. If it takes Jim 10 hours to clean the house alone, how long would it take Jen to do the job alone?
:
From above information we know:
Jay & Jim have been working a total of 3 hrs,
Jen worked 2 hrs
:
Let t = time required by Jen working alone
:
Let the completed job = 1
:
3%2F6 + 3%2F10 + 2%2Ft = 1
:
Multiply equation by 30t to get rid of the denominators;
30t*3%2F6 + 30t*3%2F10 + 30t*2%2Ft = 30t(1)
:
Cancel out the denominators and you have;
5t(3) + 3t(3) + 30(2) = 30t
:
15t + 9t + 60 = 30t
:
24t + 60 = 30t
:
60 = 30t - 24t
:
60t = 6t
t = 60%2F6
t = 10 hrs Jen working alone
:
:
Check solution in original equation
3%2F6 + 3%2F10 + 2%2F10 = 1