Question 1121267: The Tran family and the Moore family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 25 L per hour. The water output rate for the Moore family's sprinkler was 35 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1675 L.How long was each sprinkler used?
Found 3 solutions by solver91311, ikleyn, josgarithmetic:
Answer by solver91311(24713)   (Show Source):
Answer by ikleyn(52852)  (Show Source):
You can put this solution on YOUR website! .
Similar problems were solved more than 29 times in this forum.
So, next time, when you see this combination of words "family each used their sprinklers last summer", take them as a keyword
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You will get a number of solved similar problems
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https://www.algebra.com/algebra/homework/equations/Equations.faq.question.739862.html
https://www.algebra.com/algebra/homework/Expressions-with-variables/Expressions-with-variables.faq.question.1088693.html
This theme is/was so popular that I prepared special lesson
- The Robinson family and the Sanders family each used their sprinklers last summer
in this site to have a permanent link.
H a p p y l e a r n i n g ! !
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So, since you can find algebraic solution samples everywhere, let me show, instead, how to solve the problem MENTALLY,
without using equations (in a recreational mode).
Let assume for a minute that only Tran family consumed water for 55 hours.
Then the total consumed water volume would be 25*55 = 1375 liters,
which makes the shortage of 1675 - 1375 = 300 liters comparing with the given volume of 1675 liters.
Hence, in my solution we should replace the portion of 25 L by the portion of 35 L some number of times to compensate the difference.
At each such replacement, we diminish the difference of 300 liters by 35-25 = 10 liters.
So, exactly  = 30 such replacements are required.
It means that the Moore family used sprinklers for 30 hours; while the Tran family used sprinkles for the rest (55-30) = 25 hours.
Check. 25*25 + 30*35 = 1675 liters. ! Correct !
This chain of logic arguments can be packed and replaced by this "one line formula"
Moore family time =  = 30 hours.
If you learn this logic/mental solution, then you will be able to solve similar problems by using this "one line formula" method.
By doing it in this way, you will impress your teacher and your classmates !
They will consider you as a magician ! ! !
Answer by josgarithmetic(39625)  (Show Source):
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