Francisco and Michael are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Francisco is 340 miles away from the stadium and Michael is 220 miles away from the stadium. Francisco is driving along the highway at a speed of 70 miles per hour and Michael is driving at speed of 30 miles per hour. Let F represent Francisco's distance, in miles, away from the stadium t hours after noon. Let M represent Michael's distance, in miles, away from the stadium t hours after noon. Graph each function and determine whether Francisco or Michael is closer to the stadium 2 hours after noon.
First, let's set up the functions for F and M:
F(t) = 340 - 70t
M(t) = 220 - 30t
Now let's graph both functions on the same coordinate plane:
- Francisco's function: F(t) = 340 - 70t
- Michael's function: M(t) = 220 - 30t
Now, let's determine who is closer to the stadium 2 hours after noon:
F(2) = 340 - 70(2) = 340 - 140 = 200
M(2) = 220 - 30(2) = 220 - 60 = 160
Therefore, 2 hours after noon, Michael is closer to the stadium, as he is 160 miles away compared to Francisco who is 200 miles away.