Question 1017313: Because of an anticipated heavy rain storm a reservoir needs to be lowered by 1 foot. If spillway A is opened the reservoir will lose 1 foot every four hours, but if reservoir B is opened the reservoir will lose 1 foot every 6 hours. How long will it take to lose 1 foot if Both reservoirs are opened at the same time?
**** I just need someone to help walk me through setting up this problem algebraically. I can calculate the answer to be 2.4 hours in my head but i can't for the life of me figure out how to set it up algebraically. Thank You!
Answer by josgarithmetic(39625)   (Show Source):
You can put this solution on YOUR website! Job rates problem, RT=J to relate flow rate, time, amount of job.
ONE job is to lower the water level by 1 foot.
Look at the individual and combined rates of the spillways.
A 
B 
A&B 
Spillways A and B combined, operating simultaneously lower the level at the rate
 feet per hour, or 5 feet in every 12 hours.
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You can convert into INCHES per HOURS if you want, and then work within the inch unit only for the "length" or level. The conversion is simple, and you already know how to do it - so your extra question will also be seen as very simple, if you will just try.  , truly IS  .
Re-examine very carefully, that the "equation" I gave was RT=J for flow rate, time, and amount of job, and "one job" was "lower water level by 1 foot". You CAN, if you wanted, interpret the situation as travel rates, and say, RT=D for rate, time, and DISTANCE. Now, either way, you know R, you know D, and you wish to calculate T. Keep in units of feet and hours, without any conversion into inches.
 , using variable t, as the amount of time.
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