SOLUTION: Lala and Baba can finish stacking 200 cups together in 12/5 hrs. One day, Baba stacked by herself. An hour later, Lala joined and they finished the job in 9/5 hrs. If Lala works al

Question 885611: Lala and Baba can finish stacking 200 cups together in 12/5 hrs. One day, Baba stacked by herself. An hour later, Lala joined and they finished the job in 9/5 hrs. If Lala works alone and stacks all 200 cups, how many hours would it take her?
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The ONE job is to stack 200 cups.

Lala AND Baba, jobs per hour
Lala, unknown, jobs per hour for some unknown L hours
Baba, unknown, jobs per hour for unknown time L.
-
Baba for 1 hour and then both for the hours for doing 1 job:

-
You can also form an equation for the sum of the combined rates of Baba and Lala:

-
Those are two linear equations (they will be more obviously when you simplify them) in two unknowns, L and B. Just solve the system. L is the time for Lala to do the one job alone and B is the time for Baba to do the job alone.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = Baba's rate of stacking in cups/hr
Let = Lala's rate of stacking in cups/hr
Let cups stacked = 1 job
-----------------------
Add their rates of stacking to get rate stacking together
(1)
(1)
(1)
--------------------------------
In 1 hr, Baba stacked:
cups
The fraction of the job left to do is:

--------------
(2)
--------------------------------------
Multiply both sides of (2) by
(2)
(2)
(2)
(2)
------------------------
I can say:
(1)
(1)
(1)
------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
and
(2)
(2)
Working alone, it takes Lala 6 hrs
-----------------------
check:
(1)
(1)
(1)
OK
also:
(2)
(2)
(2)
(2)
OK

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Lala and Baba can finish stacking 200 cups together in 12/5 hrs. One day, Baba stacked by herself. An hour later, Lala joined and they finished the job in 9/5 hrs. If Lala works alone and stacks all 200 cups, how many hours would it take her?

It'll take Lala hours to stack cups by herself.
You can do the check!!
If you need a complete and detailed solution, let me know!!
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