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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 964529: 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?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
=================
Use a set of equations of rates to get:
j + p = 1/2 job/hr
p + L = 3/5 job/hr
j + p + L = 1/1 job/hr
------------------------------
Substitute for "j" and for "L" and solve for "p"::
(1/2)-p + p + (3/5)-p = 1
Simplify::
(1/2)+(3/5) - p = 1
-----
(5+6)/10 - p = 1
-p = -1/10
p = 1/10 (Penny's rate)
----
Solve for "J"
j + p = 1/2
j + 1/10 = 1/2
----
j = (5/10) - (1/10)
j = 4/10 = 2/5 (Jenny's rate)
------
Ans:: Jenny's time to do the job alone:: 5/2 = 2 1/2 hrs
--------------------
Cheers,
Stan H.
--------------
------------