SOLUTION: Word problems are my toughest challenge. For example; Draining the vat. With only the small valve open, all of the liquid can be drained from a large vat in 4 hours. With only

Question 196839: Word problems are my toughest challenge. For example;
Draining the vat. With only the small valve open, all of
the liquid can be drained from a large vat in 4 hours. With
only the large valve open, all of the liquid can be drained
from the same vat in 2 hours. How long would it take to
drain the vat with both valves open? How do I figure out the time it takes to drain the vat? Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Draining the vat.
With only the small valve open, all of the liquid can be
drained from a large vat in 4 hours.
Time = 4 hrs/job ; Rate = 1/4 job/hr
--------------------------------------------
With only the large valve open, all of the liquid can be drained
from the same vat in 2 hours.
Time = 2 hrs/job ; Rate = 1/2 job/hr.
-----------------------------------------------
How long would it take to drain the vat with both valves open?
Time = x hrs/job ; Rate = 1/x job/hr.
------------------------------------------------
Equation:
rate + rate = together rate
1/4 + 1/2 = 1/x
Multiply thru by 4x to get:
x + 2x = 4
3x = 4
x = 4/3 hr
x = 1 hr and 20 minutes (time to do the job when both vales are open)
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Cheers,
Stan H.
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