SOLUTION: IT CAN TAKE 12 HOURS TO FILL A SWIMMING POOL USING 2 PIPES.IF THE PIPE OF LARGER DIAMETER IS USED FOR 4 HOURS,THE PIPE OF SMALLER DIAMETER IS USED FOR 9 HOURS,ONLY HALF OF THE POOL
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Question 343393: IT CAN TAKE 12 HOURS TO FILL A SWIMMING POOL USING 2 PIPES.IF THE PIPE OF LARGER DIAMETER IS USED FOR 4 HOURS,THE PIPE OF SMALLER DIAMETER IS USED FOR 9 HOURS,ONLY HALF OF THE POOL CAN BE FILLED.HOW LONG WOULD IT TAKE FOR EACH PIPE TO FILL THE POOL SEPERATELY?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
IT CAN TAKE 12 HOURS TO FILL A SWIMMING POOL USING 2 PIPES.
IF THE PIPE OF LARGER DIAMETER IS USED FOR 4 HOURS,THE PIPE OF SMALLER
DIAMETER IS USED FOR 9 HOURS, ONLY HALF OF THE POOL CAN BE FILLED.
HOW LONG WOULD IT TAKE FOR EACH PIPE TO FILL THE POOL SEPARATELY?
:
Let a = larger pipe time to fill the pool by itself
Let b = smaller pipe time to fill it
:
Let a full pool = 1
then
half full pool = .5
:
Write an equation for each statement:
;
"It can take 12 hr to fill a swimming pool using 2 pipes"
+ = 1
:
"If the larger pipe is used for 4 hrs and the smaller pipe for 9 hrs, only half
the pool will be filled"
+ = .5
:
Use elimination, multiply the above equation by 3, subtract the 1st equation
+ = 1.5
+ = 1
------------------------------subtraction eliminates a find b
= .5
15 = .5b
b = 30 hrs for the small pipe alone
:
Find a using the 1st equation
+ = 1
Multiply by 30a
30(12) + 12a = 30a
360 = 30a - 12a
360 = 18a
a =
a = 20 hrs for the large pipe alone
:
:
Confirm this in the 2nd equation
+ =
.2 + .3 = .5
:
:
Summarize: the large pipe requires 20 hr alone, the small pipe 30 hrs alone
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