Question 98431
A sink is filling at the rate of 1 liter in 5 seconds. It is draining at the rate of 1 liter in 11 seconds. How long for the time it is empty will it take the sink to fill, if its capacity is 8 liters?
:
Let's look the two devices individually
The faucet alone fills the sink: 8 * 5 = 40 sec
The drain alone empties a full sink: 8 * 11 = 88 sec
:
Let t = time to fill the sink when both devices are on
Let the full sink = 1
Filling is +
Draining is -
:
{{{t/40}}} - {{{t/88}}} = 1
:
Multiply equation by 880
880*{{{t/40}}} - 880*{{{t/88}}} = 880(1)
:
CAncel out the denominators and you have:
22t - 10t = 880
:
12t = 880
:
t = 880/12
:
t = 73.33 seconds
:
:
Check using t = 73.33 :
{{{73.33/40}}} - {{{73.33/88}}} = 1
 1.83 - .83 = 1
:
How about this? Was it understandable?