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

Algebra ->  Rate-of-work-word-problems -> 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       Log On


   

Question 260492: 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?
[hint: Let x be the time taken by George. How much of the lawn does George mow in 1 hour? How much does Henry do in 1 hour? How much do they mow together in 1 hour?]
Answer by ankor@dixie-net.com(22740) About Me  (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 for Henry to do the job by himself
then
(x+1) = time for George to do it
:
Let the completed job = 1 (a mowed lawn)
:
Change 1 hr 12 min to 1.2 hrs
;
A shared work equation
1.2%2Fx + 1.2%2F%28%28x%2B1%29%29 = 1
:
Multiply equation by x(x+1) to get rid of the denominators, 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
:
A quadratic equation
x^2 + x - 2.4x - 1.2 = 0
x^2 - 1.4x - 1.2 = 0
:
Fortunately this will factor!
(x - 2)(x + .6) = 0
:
positive solution is what we want here:
x = 2 hrs for Henry to do the job alone
;
;
Check solution on a calc, (George takes 3 hrs)
1.2/2 + 1.2/3 =
.6 + .4 = 1