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Scott begins mountain biking at sea level. He bikes up 10 feet every minute. How many minutes will it take his to reach an elevation of 70 feet? Write an expression to show Scott bikes up 10 feet every minute. Use \( m \) to represent the number of minutes. \( \square \) \( =70 \) \( -70 \) m \( -10 \) 10

Ask by Little Davies. in the United States
Jan 22,2025

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Answer

It will take Scott 7 minutes to reach an elevation of 70 feet.

Solution

To determine how long it will take Scott to reach an elevation of 70 feet while biking up at a rate of 10 feet per minute, let's break it down step by step. ### 1. **Setting Up the Expression** Let \( m \) represent the number of minutes Scott bikes. Since Scott gains 10 feet every minute, the total elevation \( E \) he reaches after \( m \) minutes can be expressed as: \[ E = 10m \] ### 2. **Solving for \( m \) When \( E = 70 \) Feet** We want to find out how many minutes \( m \) it takes for Scott to reach 70 feet. Plugging \( E = 70 \) into the equation: \[ 10m = 70 \] To solve for \( m \), divide both sides of the equation by 10: \[ m = \frac{70}{10} = 7 \] ### **Conclusion** - **Expression:** \( 10m = 70 \) - **Number of Minutes:** It will take Scott **7 minutes** to reach an elevation of 70 feet.

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The Deep Dive

To express Scott's progress in biking up, you can write the equation \( 10m = 70 \) where \( m \) is the number of minutes it takes to reach 70 feet. To find \( m \), simply solve the equation by dividing 70 by 10, leading us to \( m = 7 \). So, in just 7 minutes, he'll enjoy the view from 70 feet up! Now, if you want to avoid miscalculations in future mountain biking adventures, double-check your units! Always remember that the time spent biking and the distance climbed must be in compatible forms. It’s easy to mix minutes with feet if you’re not careful; just keep your eyes on the trail and bike safely!

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