SOLUTION: ron takes two hours more than paul to mow the lawn . working togather they can mow the lawn in 5 hrs . how long does it take each of them working alone

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Question 109329: ron takes two hours more than paul to mow the lawn . working togather they can mow the lawn in 5 hrs . how long does it take each of them working alone
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fx + 5%2F%28%28x%2B2%29%29 = 1
:
Multiply equation by x(x+2) to get rid of the denominators:
x(x+2)*5%2Fx + x(x+2)*5%2F%28%28x%2B2%29%29 = 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)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
ron takes two hours more than paul to mow the lawn.
working togather they can mow the lawn in 5 hrs. 
how long does it take each of them working alone?

Make this chart:


       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron      

Paul      

Both      


We are interested in Ron mowing 1 lawn, Paul mowing 1 lawn,
and both working together to mow 1 lawn.  So we put 1 for
the number of lawns mowed in all three cases:


       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron       1                                          

Paul      1                                      

Both      1                                      


Now let "t" equal the time Paul takes to mow 1 lawn. So
put t as Paul's time:



       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron       1                                      

Paul      1                                      t 

Both      1                                       


>>...ron takes two hours more than paul to mow the lawn...<<

So we add 2 to Paul's time to get Ron's time. So put t+2
for Ron's time:

       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron       1                                     t+2 

Paul      1                                      t

Both      1                                      


>>...working togather they can mow the lawn in 5 hrs...<<

So put 5 for the time for both wotking together:

       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron       1                                     t+2 

Paul      1                                      t

Both      1                                      5

 Now fill in the rates as fraction of the lawn per hour by dividing
 the number of lawns mowed by the time required. 

       number of     rate as fraction of    time required to
      lawns mowed    lawn mowed per hour        mow                 
Ron       1              1%2F%28t%2B2%29                 t+2 
Paul      1               1%2Ft                     t
Both      1               1%2F5                     5

We form the equation this way:

Ron's rate + Paul's rate = their combined rate when both work together.

            1%2F%28t%2B2%29 + 1%2Ft = 1%2F5     

Can you solve that by getting LCD of 5t(t+1). It's leads to a quadratic
equation that does not factor and you have to use the quadratic
formula.  You get two solutions, approximately

t = 9.099019514 and t = -1.099019514 and we ignore the negative one,

so it takes Paul 9.099019514 hours to mow the lawn and it takes
Paul 2 hours more or  11.099019514 hours.

It's either a very huge lawn or they are very slow mowers.

Edwin