SOLUTION: A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 1 hour to fill the tank with the large inlet pipe. On the other hand, it takes 6

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 1 hour to fill the tank with the large inlet pipe. On the other hand, it takes 6       Log On


   

Question 742380: A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 1 hour to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours. What fraction of the tank (initially empty) will be filled in 0.98 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
b = rate of big pipe
s = rate of small pipe
e = rate for outlet pipe, which empties the tank
Rates are in TANK per HOUR, and rates are additive. e%3C0 because it works in the opposite direction from b and s.

b+=+1%2F1=1+
s+=+1%2F6
e+=+-1%2F7

All three pipes begin operating together at a time the tank is initially empty. How much of the tank will be filled in 0.98 hours?
R%2Ah=j, where R is the combined rates of the three pipes, h is time in hours, and j is the amount of the job of filling the tank (which we expect to be positive).

%28b%2Bs%2Be%29%2Ah=j
%28b%2Bs%2Be%29%2A0.98=j, find j.
highlight%28%281%2B1%2F6%2B%28-1%2F7%29%29%2A%280.98%29=j%29
%281%2B1%2F6-1%2F7%29%2A%280.98%29=j
%28%2842%2B7-6%29%2F42%29%2A%280.98%29=j
highlight%28%2843%2F42%29%280.98%29=j%29

j=1.00 to the nearest hundredth place. This did not render as needed, so,..
j=1.00____ to the nearest hundredth place. This system does not render the way it should. That should appear as, "One point zero zero".