Question
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?
Answers
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
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(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
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
Related Questions
They have emptied 1/2 to an oil tank; then they emptied another half of what was left; then the rest...
a woman is draining her fish tank by siphoning the water into an outdoor drain the rectangular tank...
A water tank is being slowly emptied to remove it and replace it with another one. The graph shows t...
Use the image to answer the question.
A water tank is being slowly emptied to remove it and...