An empty pool is filled using two hoses. Hose A delivers 15... | SAT Linear equations in two variables Question, Answer Explained

Question bank / Linear equations in two variables

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An empty pool is filled using two hoses. Hose A delivers $15$ gallons per minute, and hose B delivers $25$ gallons per minute. The equation $15a + 25b = 2{,}400$ represents the numbers of minutes, $a$ and $b$ , that hoses A and B run to fill the pool with $2{,}400$ gallons. If hose A runs for $40$ minutes, for how many minutes must hose B run to fill the pool?

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Answer: 72

Substitute $a = 40$ : $15(40) + 25b = 2{,}400$ , so $600 + 25b = 2{,}400$ . Then $25b = 1{,}800$ and $b = 72$ .

Dividing $2{,}400$ by $25$ gives $96$ , the time hose B would need alone, which ignores the $600$ gallons from hose A.

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