algebra
posted by carolyn on .
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?

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 
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(xy) = 1
x  y = 1/6
drain closed: 30y = 1
y = 1/30
plug back into xy = 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