Genesis and Skylar are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Genesis is 266 miles away from the stadium and Skylar is 332 miles away from the stadium. Genesis is driving along the highway at a speed of 42 miles per hour and Skylar is driving at speed of 53 miles per hour. Let GG represent Genesis' distance, in miles, away from the stadium tt hours after noon. Let SS represent Skylar's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t, commat, and determine the number hours after noon, t, commat, when Genesis and Skylar are the same distance from the stadium.
The equation for Genesis' distance from the stadium after t hours can be written as:
GG = 266 - 42t
The equation for Skylar's distance from the stadium after t hours can be written as:
SS = 332 - 53t
To find the number of hours after noon when Genesis and Skylar are the same distance from the stadium, we need to set GG equal to SS and solve for t:
266 - 42t = 332 - 53t
Adding 53t to both sides of the equation:
266 + 11t = 332
Subtracting 266 from both sides of the equation:
11t = 66
Dividing both sides of the equation by 11:
t = 6
Therefore, Genesis and Skylar will be the same distance from the stadium 6 hours after noon.