Hailey and Levi are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Hailey is 300 miles away from the stadium and Levi is 450 miles away from the stadium. Hailey is driving along the highway at a speed of 25 miles per hour and Levi is driving at speed of 50 miles per hour. Let HH represent Hailey's distance, in miles, away from the stadium tt hours after noon. Let LL represent Levi's distance, in miles, away from the stadium tt hours after noon. Graph each function and determine how far both Hailey and Levi are from the stadium at the moment they are an equal distance from the stadium.

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oeerivona oeerivona · Answer 1 · 2021-12-22T11:01:30+01:00

The distance Hailey and Levi are from the stadium as they drive, can be

shown using a graph.

Please find attached the graph of the function of Hailey's and Levi's distance from the stadium, created with MS Excel.

The distance they both are from the stadium at the moment they are at an equal distance from the stadium is 150 miles.

Reasons:

The given information are;

Distance of Hailey from the stadium at noon = 300 miles

Distance of Levi from the stadium at noon = 450 miles

Hailey's speed = 25 mph

Levi's speed = 50 mph

Required:

(a) Draw the graph of the function of their distance from the stadium

(b) Determine the distance how far from the stadium at which they are at an equal distance from the stadium.

Solution:

Based on the question, the required function are;

Hailey's distance from the stadium, H = 300 - 25·t

Levi's distance from the stadium, L = 450 - 50·t

The graph of the distance of Hailey and Levi can be plotted on MS Excel using the above functions.

At the time they are equal distance from the stadium, we have;

H = L

Which gives;

300 - 25·t = 450 - 50·t

50·t - 25·t = 450 - 300 = 150

25·t = 150

[tex]\displaystyle t = \frac{150}{25} = 6[/tex]

Therefore, after 6 hours, Hailey and Levi are at an equal distance from the stadium.

The distance from the stadium, d = 300 - 25 × 6 = 150

The distance both Hailey and Levi are from the stadium, the moment they are an equal distance from the stadium, d = 150 miles

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