A hot air balloon descends at a constant rate. The function... | SAT Linear functions Question, Answer Explained

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A hot air balloon descends at a constant rate. The function $h(t) = 1{,}800 - 45t$ gives the balloon's height, in feet, $t$ minutes after it begins its descent. How many minutes after it begins its descent is the balloon at a height of $720$ feet?

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Answer: 24

Set $h(t) = 720$ : $1{,}800 - 45t = 720$ . Subtract $1{,}800$ from both sides: $-45t = -1{,}080$ . So $t = 24$ .

Dividing $720$ by $45$ gives $16$ , but $720$ feet is the height the balloon reaches, not the distance it has descended.

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