SOLUTION: Alicia can complete a certain project in 5 more hours than her brother Alex if they work together they can finish the job in 6 hours, How long would it take each one of them to com

Algebra ->  Human-and-algebraic-language -> SOLUTION: Alicia can complete a certain project in 5 more hours than her brother Alex if they work together they can finish the job in 6 hours, How long would it take each one of them to com      Log On


   

Question 754070: Alicia can complete a certain project in 5 more hours than her brother Alex if they work together they can finish the job in 6 hours, How long would it take each one of them to complete the project?\
Can you please help me out ? Thanks so much in advance:)
Can you also please show the steps it would really help me understand better:)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Alicia can complete a certain project in 5 more hours than her brother Alex
if they work together they can finish the job in 6 hours, How long would it take each one of them to complete the project?\
:
Let x = time required by Alex to do the job
It says,"Alicia can complete a certain project in 5 more hours than
her brother". Therefore
(x+5) = time required by Alicia to do the job
:
let the completed job = 1
:
Write a shared work equation, each does a fraction of the job
the two fractions add up to 1
:
6%2Fx + 6%2F%28%28x%2B5%29%29 = 1
Multiply by x(x+5), cancel the denominators, and you have:
6(x+5) + 6x = x(x+5)
6x + 30 + 6x = x^2 + 5x
Combine as a quadratic equation on the right:
0 = x^2 + 5x - 12x - 30
x^2 - 7x - 30 = 0
Factors to
(x-10)(x+3) = 0
The positive solution is all we want here
x = 10 hrs required by Alex
then
15 hrs required by Alicia
:
:
See if this checks out
6%2F10 + 6%2F15 =
.6 + .4 = 1; confirms our solution