SOLUTION: It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take Henry

Question 256346: It takes George 1 hour longer to mow the lawn than it takes Henry. Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes. How long would it take Henry to mow the lawn by himself?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It takes George 1 hour longer to mow the lawn than it takes Henry.
Working together, using two mowers, they can mow the lawn in 1 hour and 12 minutes.
How long would it take Henry to mow the lawn by himself?
:
Let x = time required by Henry to mow the lawn by himself
It say,"George 1 hr longer", therefore
(x+1) = time required by George
:
Change 1 hr 12 min to 1.2 hrs
:
Let completed job = 1
:
A shared work equation
+ = 1
Multiply equation by x(x+1), results:
1.2(x+1) + 1.2x = x(x+1)
:
1.2x + 1.2 + 1.2x = x^2 + x
:
2.4x + 1.2 = x^2 + x
Arrange as a quadratic equation
x^2 + x - 2.4x - 1.2 = 0
:
x^2 - 1.4x - 1.2 = 0
Factors to
(x-2)(x+.6) = 0
Positive solution
x = 2 hrs, Henry by himself
:
:
Check solution on a calc
+ =
.6 + .4 = 1
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