SOLUTION: Please help me understand how to solve these word problems. Not just get the answers but a better understanding. Working together, Aaron and Rosa can mow the lawn around the loc

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Question 1030790: Please help me understand how to solve these word problems. Not just get the answers but a better understanding.
Working together, Aaron and Rosa can mow the lawn around the local library in 3 hours. Working alone Aaron can mow the lawn in 5 hours. Write and solve an equation to determine how long it would take Rosa to mow by herself.
Found 4 solutions by mananth, rothauserc, ikleyn, MathTherapy:
Answer by mananth(16946) About Me  (Show Source):
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Working together, Aaron and Rosa can mow the lawn around the local library in 3 hours. Working alone Aaron can mow the lawn in 5 hours. Write and solve an equation to determine how long it would take Rosa to mow by herself.

Working alone Aaron can mow the lawn in 5 hours
Aaron does 1/5 of the job in 1 hour
Working alone rosa can mow the lawn in x hours
Rosa does 1/x of the job in 1 hour
Working together, Aaron and Rosa can mow the lawn around the local library in 3 hours.
They do 1/3 of the job in 1 hour
1/5 + 1/x = 1/3
1/x = 1/3 -1/5
1/x = 2/5
x= 5/2
Working alone Aaron can mow the lawn in 2 hours 30 minutes

Answer by rothauserc(4718) About Me  (Show Source):
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Aaron mows the lawn in 5 hours, so he does 1/5 of the job per hour. Let x be the number of hours Rosa takes to mow the lawn, then
:
1/5 + 1/x = 1/3
:
multiply both sides of the = by 15x
:
3x + 15 = 5x
:
2x = 15
:
x = 7.5
:
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It takes Rosa 7 1/2 hours to mow the lawn
*****************************************
:

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
You can find many other similar solved problems in the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
in this site.

Read them and you will learn how to solve such problems once and for all.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me understand how to solve these word problems. Not just get the answers but a better understanding.
Working together, Aaron and Rosa can mow the lawn around the local library in 3 hours. Working alone Aaron can mow the lawn in 5 hours. Write and solve an equation to determine how long it would take Rosa to mow by herself.
Rosa takes 7.5 hours