SOLUTION: To finish one task, Cathy need 2 more days than Mike.Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task. How many days does Cath

Algebra ->  Rate-of-work-word-problems -> SOLUTION: To finish one task, Cathy need 2 more days than Mike.Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task. How many days does Cath      Log On


   

Question 540708: To finish one task, Cathy need 2 more days than Mike.Cathy worked on it for 3 days, then Mike worked on it another 4 days. They only finish 80% of the task. How many days does Cathy need to finish the task alone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
To finish one task, Cathy need 2 more days than Mike.
Cathy worked on it for 3 days, then Mike worked on it another 4 days.
They only finish 80% of the task.
How many days does Cathy need to finish the task alone.
:
Let t = no. of days required by Cathy working alone
then
(t-2) - no. of days required by Mike
:
Let the completed job = 1
then
.8 = 80% of the job
:
The equation for the statement:
"Cathy worked on it for 3 days, then Mike worked on it another 4 days.
They only finish 80% of the task."
3%2Ft + 4%2F%28%28t-2%29%29 = .8
:
multiply by t(t-2), results
3(t-2) + 4t = .8t(t-2)
3t - 6 + 4t = .8t^2 - 1.6t
7t - 6 = .8t^2 - 1.6t
0 = .8t^2 - 1.6t - 7t + 6
:
A quadratic equation
.8t^2 - 8.6x + 6
:
Get rid of those decimals, mult by 10
8t^2 - 86t + 60 = 0
;
Simplify, divide by 2
4t^2 - 43t + 30 = 0
:
Factors to:
(4t - 3)(t - 10) = 0
Two solutions
4t = 3
t = 3/4
t = .75
and
t = 10 hrs is the reasonable answer for Cathy's time alone
:
:
Check solution (Mike's time is 8 hrs
3%2F10 + 4%2F8 =
.3 + .5 = .8