Question

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Joan is hiking. She wants to cover 1,600 feet. She hikes 600 feet every 3 hours.

The equation of the line that models y, the distance left to hike, after hiking for x hours is y = ( ) + ( ). it will take ( )
hours to hike 1,600 feet.

Answer the blanks that look like this -> ( )

Answer 1

The equation of the line that models the distance left to hike, after hiking for x hours is y = 1,600 - 200x. It will take Joan 8 hours to hike 1,600 feet.

Step-by-step explanation:

Joan is hiking and wants to cover a distance of 1,600 feet, with a rate of 600 feet every 3 hours. To model this situation, we use a linear equation where y represents the distance left to hike and x represents the number of hours hiked. Since Joan covers 600 feet every 3 hours, the rate is 200 feet per hour.

To find the equation of the line, we start with the total distance to hike (1,600 feet) and subtract the distance hiked over time (200x feet/hour * hours). This gives us the equation y = 1,600 - 200x.

To determine the total time x it will take Joan to hike 1,600 feet, we set y to 0 (as this is when there is no distance left to hike) and solve for x:

1. Set the equation to 0: 0 = 1,600 - 200x.
2. Solve for x: x = 1,600 / 200.
3. Calculate x: x = 8.

So, it will take Joan 8 hours to hike 1,600 feet.