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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The ONE job is to stack 200 cups.

Lala AND Baba, 1%2F%2812%2F5%29 jobs per hour
Lala, unknown, 1%2FL jobs per hour for some unknown L hours
Baba, unknown, 1%2FB jobs per hour for unknown time L.
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Baba for 1 hour and then both for the 9%2F5 hours for doing 1 job:
highlight_green%28%281%2FB%29%2A1%2B%281%2F%2812%2F5%29%29%2A%289%2F5%29=1%29
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You can also form an equation for the sum of the combined rates of Baba and Lala:
highlight_green%281%2FL%2B1%2FB=12%2F5%29
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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +R%5BB%5D+ = Baba's rate of stacking in cups/hr
Let +R%5BL%5D+ = Lala's rate of stacking in cups/hr
Let +200+ cups stacked = 1 job
-----------------------
Add their rates of stacking to get rate stacking together
(1) +R%5BB%5D+%2B+R%5BL%5D+=+1+%2F+%28+12%2F5+%29+
(1) +R%5BB%5D+%2B+R%5BL%5D+=+5%2F12+
(1) +12R%5BB%5D+%2B+12R%5BL%5D+=+5+
--------------------------------
In 1 hr, Baba stacked:
+R%5BB%5D+%2A+1+=+R%5BB%5D+ cups
The fraction of the job left to do is:
+1+-+R%5BB%5D+
--------------
(2) +R%5BB%5D+%2B+R%5BL%5D+=+%28+1+-+R%5BB%5D+%29+%2F+%28+9%2F5+%29+
--------------------------------------
Multiply both sides of (2) by +9%2F5+
(2) +%28+9%2F5+%29%2A%28+R%5BB%5D+%2B+R%5BL%5D+%29+=+1+-+R%5BB%5D+
(2) +9%2A%28+R%5BB%5D+%2B+R%5BL%5D+%29+=+5%2A%28+1+-+R%5BB%5D+%29+
(2) +9R%5BB%5D+%2B+9R%5BL%5D+%29+=+5+-+5R%5BB%5D+%29+
(2) +14R%5BB%5D+%2B+9R%5BL%5D+=+5+
------------------------
I can say:
(1) +12R%5BB%5D+%2B+12R%5BL%5D+=+14R%5BB%5D+%2B+9R%5BL%5D+
(1) +3+R%5BL%5D+=+2R%5BB%5D+
(1) +R%5BL%5D+=+%282%2F3%29%2AR%5BB%5D+
------------------------
Substitute (1) into (2)
(2) +14R%5BB%5D+%2B+9R%5BL%5D+=+5+
(2) +14R%5BB%5D+%2B+%282%2F3%29%2A9R%5BB%5D+=+5+
(2) +14R%5BB%5D+%2B+6R%5BB%5D+=+5+
(2) +20R%5BB%5D+=+5+
(2) +R%5BB%5D+=+1%2F4+
and
(2) +R%5BL%5D+=+%282%2F3%29%2A%28+1%2F4+%29+
(2) +R%5BL%5D+=+1%2F6+
Working alone, it takes Lala 6 hrs
-----------------------
check:
(1) +R%5BB%5D+%2B+R%5BL%5D+=+5%2F12+
(1) +1%2F4+%2B+1%2F6+=+5%2F12+
(1) +3%2F12+%2B+2%2F12++=+5%2F12+
OK
also:
(2) +R%5BB%5D+%2B+R%5BL%5D+=+%28+1+-+R%5BB%5D+%29+%2F+%28+9%2F5+%29+
(2) +1%2F4+%2B+1%2F6+=+%28+1+-+1%2F4+%29+%2F+%28+9%2F5+%29+
(2) +5%2F12+=+%28+3%2F4+%29%2A%28+5%2F9+%29+
(2) +5%2F12+=+5%2F12+
OK



Answer by MathTherapy(10551) About Me  (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 highlight_green%28highlight_green%284%29%29 hours to stack cups by herself.

You can do the check!! 



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