A sink can be filled by a pipe in 6 minutes but it takes 12 minutes to drain a full sink. If both the pipe and the drain are open, how long will it take to fill the sink?
ratedraining= 1sinkluff/12min
ratefilling=1sinkfull/6min
time= 1 sink/(1/12+1/6)=12*6/(6+12)=4 min
seems to me like the sink is being filled at the rate of 1/6 - 1/12 = 1/12 sink/min, so it will take 12 minutes to fill it if the drain is open.
To solve this problem, we need to find the rate at which the sink is filled by the pipe and compare it to the rate at which it is drained. Let's break it down step by step:
1. Let's assume that the capacity of the sink is represented by a certain number of units. We don't need to know the exact capacity; we'll just use units as a reference.
2. We are given that the pipe can fill the sink in 6 minutes, so the rate of filling is 1/6 of the sink's capacity per minute. This means that in 1 minute, 1/6 of the sink is filled.
3. On the other hand, we are told that the sink drains in 12 minutes, which means the rate of draining is 1/12 of the sink's capacity per minute. In 1 minute, 1/12 of the sink is drained.
4. If both the pipe and the drain are open at the same time, the effective rate of filling is determined by the difference between the pipe's filling rate and the drain's draining rate.
5. So, the net rate of filling the sink is (1/6 - 1/12) of the sink's capacity per minute.
6. Simplifying the expression, we have (2/12 - 1/12) = (1/12) of the sink's capacity per minute.
7. To fill the entire sink, we need to consider the time required, so let's denote it as 'x' minutes.
8. Now we set up an equation to describe the relationship between time and rate. The equation is:
(1/12) * x = 1
This equation states that the rate of filling (1/12 of the sink's capacity per minute) multiplied by the time (x minutes) equals the capacity of the sink (1). We want to find the value of 'x' to determine how long it takes to fill the sink.
9. To solve for 'x', we multiply both sides of the equation by 12:
x = 12
Therefore, it will take 12 minutes to fill the sink if both the pipe and the drain are open.