Question 109329
ron takes two hours more than paul to mow the lawn . working together they can mow the lawn in 5 hrs . how long does it take each of them working alone>
:
x = number of hrs required by Paul working alone:
Then
(x+2) = number of hrs required by Ron working alone
:
Let the completed job = 1
:
A simple equation:
{{{5/x}}} + {{{5/((x+2))}}} = 1
:
Multiply equation by x(x+2) to get rid of the denominators:
x(x+2)*{{{5/x}}} + x(x+2)*{{{5/((x+2))}}} = x(x+2)*1
:
Cancel out the denominators:
5(x+2) + 5x = x(x+2)
:
5x + 10 + 5x = x^2 + 2x
:
combine like terms, arrange as a quadratic equation on the left:
x^2 + 2x- 5x - 5x - 10 = 0
:
x^2 - 8x - 10 = 0
:
This won't readily factor, solve using the quadratic formula:
a = 1; b = -8; c = -10
:
I assume you know how to do that;
You should get:
x = 9.1 hrs (Paul's time)