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Question 158551: Crystal just had a swimming pool put in her backyard. When full, the swimming pool holds 52,000 gallons of water. Two water pipes are available to fill her pool, and there is a drain to empty the pool. If only pipe 1 is opened and the drain is closed, the pipe can fill the pool in 5 hours. If only Pipe 2 is opened and the drain is closed, this second pipe can fill the pool in 9 hours. Crystal is impatient; so, she opens both pipes. Unfortunately, Crystal forgets to close the drain. When both pipes are closed, this open drain can empty a full pool in 4 hours.
1: How many gallons can Pipe 1 dispense in one hour?
2: How many gallons can Pipe 2 dispense in one hour?
3: How many gallons can pour down the drain in one hour?
4: The filling rate for Pipe 1 is the answer in question 1 divided by 52,000 gallons. What is the filling rate for Pipe 1? Write answer in fraction.
5: The filling rate for Pipe 2 is the answer in question 2 divided by 52,000 gallons. What is the filling rate for Pipe 1? Write answer in fraction.
6: The draining rate for the drain is the answer in question 3 divided by 52,000 gallons. What is the draining rate? Write answer in fraction.
7: With both pipes and the drain open, write a function describing what proportion of her poos is full after t hours then simplify the function. Write answers as fractions. P(t) = ?t + ?t - ?t = ?t
8: With both pipes and the drain open, what proportion of Crystal's pool is full after 6 hours? Round answer to the nearest thousandth.
9: With both pipes and the drain open, what proportion of Crystal's pool is full after 10 hours? Round answer to the nearest thousandth.
10: With both pipes and the drain open,
A) how long will it take Crystal to fill her pool? Write your answer in hours, minutes, and seconds. (round to the nearest second)
B)to the nearest gallon, how many gallons of water went down the drain during this time? (the amount of water wasted)
If Crystal had remembered to close the drain, write a function describing what percent full her pool is after t hours then simplify the function. Write answer as fractions. P(t) = ?t + ?t = ?t
11: If Crystal had remembered to close the drain how long will it take Crystal to fill her pool? Write your answer in hours, minutes, and seconds. (Round to the nearest second)
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! OK
Pipe 1 fills the pool at the rate of 1/5 pool per hour or:
Pipe 1 fills the pool at the rate of (1/5)*52000=10400 gal per hour
Pipe 2 fills the pool at the rate of 1/9 pool per hour or:
Pipe 2 fills the pool at the rate of (1/9)*52000=5777.778 gal per hour
Together pipe 1 and pipe 2 will fill the pool at the rate of 1/5 + 1/9 pool per hour=9/45+5/45=14/45 pool per hour or:
(14/45)*52000=16177.778 gal per hour
And this checks:From above
10,400+5777.78=16,177.778 gal per hour
Now the drain empties at the rate of 1/4 pool per hour or:
The drain empties at the rate of (1/4)*52000=13,000 gal per hour
QUESTION NUMBER:
(1) 10,400 gal/hr
(2) You Do
(3) You Do
(4) 10400/52000=1/5 pool per hour
(5) You do
(6) You do
(7) t/5 +t/9-t/4=
(36t/180)+(20t/180)-(45t/180)=11t/180
(8)If t=6; (11*6)/180=66/180=33/90=11/30=
0.367 of her pool is full after 6 hours
(9)If t=10; (11*10)/180=110/180=11/18=
0.611 of her pool is full after 10 hours
(10A) Go back to (7):
11t/180=1(1 pool that is) multiply each side by 180
11t=180 divide each side by 11
t=16.3636 hours=16 hours 21.816 min (YOU DO THE SECONDS)
(10B) Use the answers from 10A AND also FROM (3)
NOW, I THINK THAT YOU CAN DO THE REST---but if you need more help, let me know.
HOPE THIS HELPS---PTAYLOR
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