SOLUTION: Using a new lawn mower, Abby can mow the lawn in 2 hours. Her sister Carla uses an older mower and takes 3 huors to mow the same lawn. How long will it take them if they work toget

Algebra.Com
Question 132055: Using a new lawn mower, Abby can mow the lawn in 2 hours. Her sister Carla uses an older mower and takes 3 huors to mow the same lawn. How long will it take them if they work together? Please tell me how you answer it. That would be awesome.
Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Since Abby can mow the lawn in 2 hours, that means that each hour she does 1/2 of the lawn.
.
Since Carla mows the lawn in 3 hours, each hour she mows she does 1/3 of the lawn.
.
If they work together for T hours then for completing the 1 job it will take them:
.
(1/2)*T + (1/3)*T = 1
.
You can factor the T and the equation becomes:
.
T*(1/2 + 1/3) = 1
.
1/2 equals 3/6 and 1/3 = 2/6. Substituting these equivalent values into the equation results
in:
.
T*(3/6 + 2/6) = 1
.
Since the two fractions now have the same denominator, they can be combined by adding their
numerators over the common denominator ... and this makes the equation become:
.
T*5/6 = 1
.
Get rid of the denominator 6 by multiplying both sides of the equation by 6 to convert the
equation to:
.
T*5 = 6
.
Solve for T by dividing both sides of the equation by 5 and you have:
.
T = 6/5 = 1.2
.
and 1.2 hours is the same as 60 minutes times 1.2 which is 72 minutes. And 72 minutes is
1 hour and 12 minutes.
.
So working together the two ladies can mow the complete lawn in 1 hour and 12 minutes.
.
Hope this helps you to understand the problem a little better.
.

RELATED QUESTIONS

Katrina can mow the lawn in 2 hours. It takes her brother 3 hours to mow the lawn. When... (answered by stanbon)
When Mike uses a riding mower, it takes him 3 hours to mow his lawn. When he uses a push (answered by ewatrrr)
Lynn can mow the lawn in 3 hours using a riding lawn mower. Her brother can mow the... (answered by venugopalramana)
lynn can mow the lawn in 3 hours using a riding lawn mower. Her brother can mow the same (answered by checkley71)
I want to mow my lawn this summer but I need a new lawn mower. I can choose a riding... (answered by stanbon)
Sidney can mow the law in 4 hours using her riding mower. Her son can mow the same lawn... (answered by richwmiller)
I want to mow my lawn this summer but I need a new lawn mower. I can choose a riding... (answered by stanbon)
i do not understand how to even start this problem. it says: With your new lawn mower, (answered by Nate,stanbon,Earlsdon)
a mother takes 64 minutes to mow a lawn when she works along using a gas mower. her... (answered by checkley77)