A sink can be filled by a pipe in 2 minutes but it takes 4 minutes to drain a full sink. if both the pipe and the drain are open, how long will it take to fill the sink?
1/2 - 1/4 = 1/x
x = 4
Check:
water comes in at 1/2 sink/minute
water drains out at 1/4 sink/minute
net flow: 1/2-1/4 = 1/4 sink/min
So, it takes 4 minutes to fill the sink
To determine how long it will take to fill the sink with both the pipe and the drain open, we need to find the net rate at which the sink is being filled.
Let's consider the rate at which the pipe fills the sink and the rate at which the drain empties the sink:
- The pipe can fill the sink in 2 minutes, so its fill rate is 1/2 of the sink per minute.
- The drain can empty the sink in 4 minutes, so its drain rate is 1/4 of the sink per minute.
To find the net rate of filling (when both pipe and drain are open), we subtract the drain rate from the pipe's rate:
Net fill rate = pipe's fill rate - drain's drain rate
= 1/2 - 1/4
= 1/4 of the sink per minute.
Now, we can determine how long it will take to fill the sink by finding the reciprocal of the net fill rate:
Time to fill the sink = 1 / net fill rate
= 1 / (1/4)
= 4 minutes.
Therefore, it will take 4 minutes to fill the sink when both the pipe and the drain are open.
To find out how long it will take to fill the sink when both the pipe and the drain are open, we need to consider their rates of filling and draining. Let's understand the rates first:
The filling rate of the pipe is 1 sink per 2 minutes (since it fills the sink in 2 minutes),
and
The draining rate of the sink is 1 sink per 4 minutes (since it takes 4 minutes to drain a full sink).
Now, we can calculate the combined rate of filling and draining when both the pipe and the drain are open:
Since the pipe fills the sink at a rate of 1 sink per 2 minutes, its rate is +1/2 sinks per minute.
On the other hand, the drain empties the sink at a rate of 1 sink per 4 minutes, so its rate is -1/4 sinks per minute.
When they are both open, we need to calculate their combined rate:
Combined rate = (pipe's rate) + (drain's rate)
= +1/2 - 1/4
= +2/4 - 1/4
= 1/4 sinks per minute
Now that we know the combined rate of filling and draining is 1/4 sinks per minute, we can calculate how long it will take to fill the sink.
Let's represent the time it takes to fill the sink as T minutes.
Since the combined rate is 1/4 sinks per minute, we can write the equation:
Rate × Time = Amount
(1/4) × T = 1 (as we want to fill one complete sink)
Simplifying the equation, we get:
T/4 = 1
Multiplying both sides of the equation by 4, we get:
T = 4
Therefore, it will take 4 minutes to fill the sink when both the pipe and the drain are open.