a tank can be filled by one pipe in 3
.5 hours and emptied by another in 4.2 hours.if both ipes are running, how long will it take to fill an empty tank?
in work problems like this, think of the amount of work each person can do in the unit of time.
if pipe a can fill the tank in 3.5 hours, then in one hour it can fill 1/3.5 of the tank.
The other pipe b can fill 1/4.2 of the tank in one hour.
So, in one hour, both pipes working together can fill up
1/3.5 + 1/4.2 = 0.5238 of the tank
So, to fill the whole tank, it will take 1/.5328 hours, or 1.90909 = 1 10/11 hours
In general, if various workers can do the job in a,b,c,... units of time, then working together they can do it in n units of time:
1/n = 1/a + 1/b + 1/c + ...
I see I misread the problem. It was answered correctly later on
To solve this problem, we need to find the rate at which each pipe fills or empties the tank, and then determine the combined rate when both pipes are running. Once we have the combined rate, we can calculate the time it takes to fill the tank.
Let's start by finding the filling rate of the first pipe:
- The first pipe can fill the tank in 3.5 hours.
- Therefore, the filling rate of the first pipe is 1 tank / 3.5 hours = 1/3.5 tank per hour = 2/7 tank per hour.
Next, let's find the emptying rate of the second pipe:
- The second pipe can empty the tank in 4.2 hours.
- Therefore, the emptying rate of the second pipe is 1 tank / 4.2 hours = 1/4.2 tank per hour = 5/21 tank per hour.
Now, let's determine the combined rate when both pipes are running:
- When both pipes are running, the filling rate of the tank is the sum of the filling rate of the first pipe and the emptying rate of the second pipe.
- So, the combined filling rate is (2/7) - (5/21) = (6/21) - (5/21) = 1/21 tank per hour.
Finally, let's calculate the time it takes to fill an empty tank:
- Since the rate is 1/21 tank per hour, it will take 21 hours to fill the tank completely.
So, if both pipes are running, it will take 21 hours to fill an empty tank.