SOLUTION: Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 2/3 hours. All three together can eat a w

Question 1068277: Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 2/3 hours. All three together can eat a whole gallon of ice cream together in 1 hour. How many hours would it take Jenny to eat a whole gallon of ice cream all by herself?
My Question: I know there is already a post on this.Unfortunately, I did not understand where their equations were derived from. It would be nice if you could specify there and be detailed. Thanks in advance!
Found 2 solutions by Fombitz, ikleyn:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Rate x Time = Output
Let say that eating a gallon of ice cream requires an output (or input) of 100 units (it's an arbitrary number, it could have been 1 or 27 or any other non-zero number).
-Jenny's rate
-Penny's rate
-Lenny's rate
So,

1.
and

2.
and

3.
Subtracting 1 from 3,

So,

and

Answer by ikleyn(52865)   (Show Source): You can put this solution on YOUR website!
.
This is the link to the solution you could not find in the archive:
https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1022112.html

Below for your convenience I copied and pasted that solution.

Let j = time for Jenny to eat a whole gallon of ice cream all by herself p = time for Penny - - - - " - - - y = time for Lenny. Then from the condition you have these three equations (standard equations for rates) + = , (1) + = , (2) ( <--- = 1 : ) + + = . (3) Now distract (2) from (3) (both sides). You will get = = . Hence, j = = hours. Answer. It will take hours for Jenny to eat a whole gallon of ice cream all by herself.

Notice: The equation (1) was not used in the solution at all.
              The corresponding part of the condition is not necessary and is excessive.

There is a wide variety of solved joint-work problems with detailed explanations in this site. See the lessons
    - Rate of work problems
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Using quadratic equations to solve word problems on joint work
    - Solving rate of work problem by reducing to a system of linear equations
    - Selected joint-work word problems from the archive
    - Joint-work problems for 3 participants
    - OVERVIEW of lessons on rate-of-work problems

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".

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