Question
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9. The water temperature at the beach started at 82 degrees, and it is rising 0.6 degrees each hour. If the water lemperature is now 85 degrees, write and solve an equation to find \( n \), the number of hours that have passed. \( 35^{\circ} \times 0.6 \)

Ask by Alexander Morgan. in the United States
Jan 24,2025

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Answer

To find the number of hours \( n \) that have passed, use the equation: \[ 82 + 0.6n = 85 \] Solving for \( n \) gives: \[ n = \frac{85 - 82}{0.6} = \frac{3}{0.6} = 5 \] So, 5 hours have passed.

Solution

Given: - Initial water temperature at the beach = 82 degrees - Water temperature is rising at a rate of 0.6 degrees per hour - Current water temperature = 85 degrees We can set up an equation to find the number of hours that have passed, denoted as \( n \). The equation can be written as: \[ 82 + 0.6n = 85 \] Now, we can solve this equation to find the value of \( n \). Solve the equation by following steps: - step0: Solve for \(n\): \(82+0.6n=85\) - step1: Move the constant to the right side: \(0.6n=85-82\) - step2: Subtract the numbers: \(0.6n=3\) - step3: Divide both sides: \(\frac{0.6n}{0.6}=\frac{3}{0.6}\) - step4: Divide the numbers: \(n=5\)

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To find how long it took for the water temperature to rise from 82 degrees to 85 degrees, we can set up the equation: \[ 85 = 82 + 0.6n \] Subtracting 82 from both sides, we get: \[ 3 = 0.6n \] Now, divide by 0.6: \[ n = \frac{3}{0.6} = 5 \] So, 5 hours have passed for the water temperature to rise to 85 degrees. If we think about real-world applications, temperature changes in bodies of water can greatly affect marine life and recreational activities. An increase in even a few degrees can impact fish spawning and other aquatic ecosystems. So next time you're at the beach, remember: it’s not just about the feel of the water! While solving equations like this, it’s easy to mismanage the arithmetic or forget to isolate \( n \) properly. A common mistake is skipping the step of subtracting initial values. Make sure each step of your operations is clear and mathematically sound so you can arrive at the correct answer without any slip-ups!

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