SOLUTION: There are two intake pipes to a large storage tank. Using the smaller pipe alone, it takes twice as long to fill the tank as it does using the larger pipe alone. The tank can be fi

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Question 182445: There are two intake pipes to a large storage tank. Using the smaller pipe alone, it takes twice as long to fill the tank as it does using the larger pipe alone. The tank can be filled in eight minutes if both pipes are used. How long will it take using only the smaller pipe? Explain your answer using mathematical models.
Answer by ankor@dixie-net.com(22740) (Show Source):
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There are two intake pipes to a large storage tank. Using the smaller pipe alone,
it takes twice as long to fill the tank as it does using the larger pipe alone.
The tank can be filled in eight minutes if both pipes are used. How long will it
take using only the smaller pipe? Explain your answer using mathematical models.
:
Let t = time required by the smaller pipe alone (in minutes)
;
It say the smaller pipe takes twice as long, therefore:
.5t = time required by the larger pipe alone
;
Let the completed job = 1 (a full tank)
:
Each pipe does a fraction of the job and the sum of those fractions = 1
:
+ = 1
multiply equation by t
2(8) + 8 = t
16 + 8 = t
t = 24 minutes the small pipe alone
:
:
Prove this: ( the larger pipe can fill it in 12 min alone)
+ =
+ = 1