Olivia and Valeria are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Olivia is 222 miles away from the stadium and Valeria is 255 miles away from the stadium. Olivia is driving along the highway at a speed of 53 miles per hour and Valeria is driving at speed of 64 miles per hour. Let O represent Olivia's distance, in miles, away from the stadium t hours after noon. Let V represent Valeria's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine whether Olivia or Valeria is closer to the stadium 2 hours after noon.

[tex]\textsf{ $\boxed{ \sf Valeria }$ is $\boxed{\sf 11 }$ miles closer to the stadium than $ \boxed{\sf Olivia }$ }\\\textsf{ 2 hours after noon}[/tex]

Step-by-step explanation:

Let's write the equations for Olivia's and Valeria's distances from the stadium in terms of time [tex]\sf t [/tex] after noon.

Olivia's distance from the stadium [tex]\sf O [/tex] after [tex]\sf t [/tex] hours can be represented as:

[tex]\sf O = 222 - 53t [/tex]

Valeria's distance from the stadium [tex]\sf V [/tex] after [tex]\sf t [/tex] hours can be represented as:

[tex]\sf V = 255 - 64t [/tex]

Now, let's find out who is closer to the stadium 2 hours after noon.

For Olivia, when [tex]\sf t = 2 [/tex]:

[tex]\sf O = 222 - 53(2) = 222 - 106 = 116 [/tex]

For Valeria, when [tex]\sf t = 2 [/tex]:

[tex]\sf V = 255 - 64(2) = 255 - 128 = 127 [/tex]

So, 2 hours after noon, Olivia is 116 miles away from the stadium, and Valeria is 127 miles away from the stadium.

Now, let's compare the distances:

[tex]\sf 127 - 116 = 11 [/tex]

Valeria is 11 miles closer to the stadium than Olivia 2 hours after noon.