Question

Gabriella and Ian are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Gabriella is 550 miles away from the stadium and Ian is 950 miles away from the stadium. Gabriella is driving along the highway at a speed of 25 miles per hour and Ian is driving at speed of 50 miles per hour. Let � G represent Gabriella's distance, in miles, away from the stadium � t hours after noon. Let � I represent Ian's distance, in miles, away from the stadium � t hours after noon. Graph each function and determine the number hours after noon, � , t, when Gabriella and Ian are the same distance from the stadium.

Answer 1

Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.

Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.

To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:

G(t) = 550 - 25t = I(t) = 950 - 50t

Combining like terms we get:

25t = 400

t = 16

So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.

To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.

It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.

Explanation: