Question 185180
please help me solve this word problem please thank you 
With only the small valve open, all of the liquid can be drained from a large vat in 4 hours. With only a 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?
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This type of problem comes up often.
You have to find a common measurement to add the 2 components.  Adding the 2 and 4 for 6 doesn't work.  It's obvious it will be less than 2 hours.2 
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The "trick" is to invert the times per vat to get work per hour.  One valve does 1/2 of the vat per hour, the other does 1/4 per hour.
Add 1/2 adn 1/4 = 3/4 vat per hour together.
Then the inverse of that is 4/3 hours per vat, = 1 hour 20 minutes.
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A shortcut is product over sum:
2*4/(2+4) = 8/6 = 4/3 hours.