SOLUTION: It takes a more experienced person 1 hour less to complete a task than it does a less experienced person. If they work together, they can complete the task in 1.2 hours. How long d

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Question 995321: It takes a more experienced person 1 hour less to complete a task than it does a less experienced person. If they work together, they can complete the task in 1.2 hours. How long does it take each person to complete the task working alone?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=time it takes less experienced person
Then this person works at the rate of 1/x of the task per hour
It takes the more experienced person (x-1) hours to complete the task
Then this person works at the rate of 1/(x-1) of the task per hour
Together, it takes 1.2 hours to complete the task
So together they work at the rate of 1/(1.2) of the task per hour
We also know that together they work at the rate of 1/x + 1/(x-1) of the task per hour
So our equation to solve is:
1/x + 1/(x-1)=1/(1.2) Multiply each term by (1.2)x(x-1)
This reduces to:
x^2-3.4x+1.2=0 quadratic in standard form and it can be factored
(x-3)(x-0.4)=0
x=3 and
x=0.4---an hour less than this is negative hours
ANS:Less experienced person takes 3 hrs
more experienced person takes 2 hrs
CK
1/3+1/2=1/(1.2)=10/12
4/12 + 6/12= 10/12
10/12=10/12
Hope this helps---ptaylor