John and Mariana are both driving along the same highway in two different cars to a stadium in a distant city. At noon, John is 208 miles away from the stadium and Mariana is 184 miles away from the stadium. John is driving along the highway at a speed of 50 miles per hour and Mariana is driving at speed of 44 miles per hour. Let J represent John's distance, in miles, away from the stadium t hours after noon. Let M represent Mariana's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine the number hours after noon, t, when John and Mariana are the same distance from the stadium.

Question

John and Mariana are both driving along the same highway in two different cars to a stadium in a distant city. At noon, John is 208 miles away from the stadium and Mariana is 184 miles away from the stadium. John is driving along the highway at a speed of 50 miles per hour and Mariana is driving at speed of 44 miles per hour. Let J represent John's distance, in miles, away from the stadium t hours after noon. Let M represent Mariana's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine the number hours after noon, t, when John and Mariana are the same distance from the stadium.

Answer 1

The equation for John's distance from the stadium is J = 208 - 50t

The equation for Mariana's distance from the stadium is M = 184 - 44t

To find when John and Mariana are the same distance from the stadium, we set J equal to M:
208 - 50t = 184 - 44t

Rearranging the equation, we get:
6t = 24
t = 4

So, 4 hours after noon, John and Mariana are the same distance from the stadium.