a tank can be filled by one pipe in 3.5 hours and emptied by another in 4.2 hours. if both pipes are running, how long will take to fill an empty tank ?
rate=amount/time
rate combined=sum of rates=1tank/3.5hr+1tank/4.2hrs
rate combined=(4.2+3.5)/(3.5*4.2) tanks/hr work this out.
time= 1tank/(above rate)
I also misread the problem. It is being emptied at 4.2 hrs.
To solve this problem, we need to find the combined rate at which the two pipes fill or empty the tank.
First, let's determine the fill rate of the first pipe. We know that the pipe can fill the tank in 3.5 hours. This means it fills 1/3.5th of the tank per hour, or 1/3.5 tank/hour.
Similarly, the second pipe can empty the tank in 4.2 hours. This means it empties 1/4.2th of the tank per hour, or 1/4.2 tank/hour.
Now, to find the combined rate when both pipes are running, we add the fill rate and the empty rate together. The combined rate is (1/3.5 - 1/4.2) tank/hour.
To find the time it takes to fill an empty tank, we divide the tank's volume by the combined rate. Let's assume the tank has a volume of 1 unit.
So, it will take 1 / (1/3.5 - 1/4.2) hours to fill an empty tank.
To simplify this expression, we can find the common denominator of 3.5 and 4.2, which is 14.
1 / (1/3.5 - 1/4.2) can be rewritten as 1 / (6/14 - 7/14) = 1 / (-1/14) = -14 hours.
The negative sign indicates that when both pipes are running, the tank will not fill but will be emptied. However, in reality, the tank cannot be emptied since both pipes cannot simultaneously operate. Therefore, it will take an infinite amount of time to fill the tank when both pipes are running.