I dont know how to solve this word problem.....The local swimming pool has two drain valves. One valve can empty the pool in 4 hours, while the other takes 6 hours to drain the pool. How quickly can the pool be drained if both valves are opened?
can someone help me?
it would be great if you showed the steps. =]
kthnxs;;
2007-06-18 17:53:08 · 9 answers · asked by Jasmine 1 in Science & Mathematics ➔ Mathematics
6x+4x=y
(the 6 and 4 are from above)
10x=y
y=volume of pool
2007-06-18 17:56:45 · answer #1 · answered by haley 2 · 0⤊ 0⤋
Ah, the old swimming pool drain problem. The key to doing these is to remember that
Volume = volume/time * time.
We use "pool" as a unit of volume.
So, for valve 1alone, Pool = pool/4 * 4 hours
and valve 2 alone, Pool = pool/6 * 6 hours.
In this problem we have TWO valves running for x number of hours.
So: 1(pool) = 1/4 x + 1/6 x = 5/12 x. Then it takes 12/5 hours or 2.4 hours to drain the pool.
2007-06-18 18:01:30 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋
First lets assume that the pool capacity is of x liters.
Then the drain speed of each valve is of:
x liters each 4 hours for the first
x liters each 6 hours for the second
To find the total time to drain x liters we just add both speeds, it is:
x (l/4h) + x (l/6h) = ¼ + 1/6 (x*l/h) = 5/12 (x*l/h) which means that both valves drain 5/12 of the pool each hour.
Therefore it will take 12/5 = 2.4 hours to drain the whole pool.
2007-06-18 18:10:42 · answer #3 · answered by Dexter H. 2 · 0⤊ 0⤋
Assume the volume of the pool is x gallons. The first valve drains at x/4 gallons per hour. The second drains at x/6 gallons per hour. So, together they drain x/6 + x/4 gallons per hour
2x/12 + 3x/12 = 5x/12 gallons per hour. That means they would drain x gallons in 12/5 hours or 2 hours and 24 minutes.
2007-06-18 18:02:03 · answer #4 · answered by Anonymous · 0⤊ 0⤋
consider the valve's rates
the first valve empties 1/4 pool/hour
second 1/6
working together, they rmpy 1/4 + 1/6 = 5/12 pool in an hour, so they empty the whole pool in 12/5 hours
= 2 hours, 24 minutes.
2007-06-18 18:01:55 · answer #5 · answered by holdm 7 · 0⤊ 0⤋
Let x = time the 2 valves can drain the pool
1/4x = the rate of the first valve
1/6x = the rate of the second valve
_______________________________
1/4x + 1/6x = 1
Multiply the equation by 12
3x + 2x = 12
5x = 12
x = 12/5
x = 2.40 hours or 2 hours and 24 minutes
2007-06-18 18:12:48 · answer #6 · answered by detektibgapo 5 · 0⤊ 0⤋
I have no steps since I did it in my head, but I believe the answer is two and a half hours...
2007-06-18 17:57:48 · answer #7 · answered by Walter . 2 · 0⤊ 0⤋
Speed is the same as that which I thought to answer the question
2007-06-18 18:00:37 · answer #8 · answered by a4tech2030 1 · 0⤊ 0⤋
2.44 hours
I think you should find out how to solve it yourself.
2007-06-18 18:00:19 · answer #9 · answered by utah-1992 1 · 0⤊ 0⤋