# algebra

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A certain toilet tank can be emptied in 6 sec through its drain when it is flushed. This happens at the same time that the water is flowing in through the inlet pipe. Withthe drain closed, the inlet pipe canfill the tank in 30 sec. How long would it take to drain the tank if the water was not flowingin through the inlet pipe?

• algebra -

in flow rate Q1 = 1 tank / 30 seconds
out flow rate = Q2

Q2 - Q1 = 1 tank/6 seconds

Q2 - 1/30 = 1/6
Q2 = 5/30 + 1/30 = 6/30 = 1/5 = 1 tank/5 seconds
so
5 seconds

• algebra -

let the tank hold 1 unit of volume

let the rate of water flowing in be y units/sec
let the water flowing out be x units / sec

When drain is open (water going in and out at the same time)
6(x-y) = 1
x - y = 1/6

drain closed: 30y = 1
y = 1/30

plug back into x-y = 1/6
x - (1/30) = 1/6
x = 1/5

only drain open:
t(1/5) = 1
t = 5 sec

With the drain only,
it would take 5 seconds to empty the tank

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