Answer:
Christian will catch up with Andrew at 4 PM.
Step-by-step explanation:
We use the equations of their positions to solve this question. This equation has the following format:
[tex]S(t) = S(0) + at[/tex]
In which S(t) is the position after t hours, S(0) is the initial position, and a is their speed.
Andrew starts walking at noon, Christian at 1.
We can model the equations starting from 1.
Andrew:
Starts at noon, 3 mph.
So at 1, when Christian starts walking, he is at the mile 3. So S(0) = 3. 3mph, a = 3. So
[tex]S_{a}(t) = 3 + 3t[/tex]
Christian:
Starts at 1, 4 mph.
So at 1, he is at the position 0. So S(0) = 0. 4 mph, so a = 4.
[tex]S_{c}(t) = 4t[/tex]
What time will Christian catch up with Andrew?
t hours after Christian starts walking(which is 1 pm).
t is found when
[tex]S_{c}(t) = S_{a}(t)[/tex]
[tex]4t = 3 + 3t[/tex]
[tex]t = 3[/tex]
3 hours after 1 PM, which is 4PM.
Christian will catch up with Andrew at 4 PM.
