SOLUTION: Kathrin and Tom together clean the garage in 3 hours. Seperatly, it takes Tom one hour more then Kathrin. How long does it take the to clean the garage seperatly? Approximate to th

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Question 195186: Kathrin and Tom together clean the garage in 3 hours. Seperatly, it takes Tom one hour more then Kathrin. How long does it take the to clean the garage seperatly? Approximate to the nearest tenth of an hour.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Kathrin and Tom together clean the garage in 3 hours.
Separatly, it takes Tom one hour more then Kathrin.
How long does it take the to clean the garage seperatly?
Approximate to the nearest tenth of an hour.
;
Let t = time required for K to do the job alone
then
(t+1) = time for T to do the same job alone
:
let the completed job = 1
:
Each will do a fraction of the job; the two fractions add up to 1
:
3%2Ft + 3%2F%28%28t%2B1%29%29 = 1
:
Multiply equation by t(t+1)
t(t+1)*3%2Ft + t(t+1)*3%2F%28%28t%2B1%29%29 = t(t+1)(1)
cancel out the denominators and you have:
3(t+1) + 3t = t(t+1)
:
3t + 3 + 3t = t^2 + t
:
6t + 3 = t^2 + t
arrange as a quadratic equation
0 = t^2 + t - 6t - 3
:
t^2 - 5t -3 = 0
Use the quadratic formula; a=1; b=-5; c=-3
:
Do math here:
t+=+%28-%28-5%29+%2B-+sqrt%28-5%5E2+-+4+%2A+1+%2A+-3+%29%29%2F%282%2A1%29+
the positive solution:
t = 5.54 hrs, is K's time alone
and
6.54 = T's time alone