Answer:
Katie will catch up to Susan after running 33.4 h.
Step-by-step explanation:
We can find the time that takes Katie to catch up to Susan by using the following equation:
[tex] x_{f_{k}} = x_{0_{k}} + v_{0_{k}}t + \frac{1}{2}at^{2} [/tex]
Where:
[tex] x_{f_{k}} [/tex]: is the final position of Katie
[tex] x_{0_{k}} [/tex]: is the initial position of Katie = 0
[tex] v_{0_{k}}[/tex]: is the initial speed of Katie = 5.2 mi/h
a: is the acceleration = 0 (she is moving at constant speed)
t: is the time
Since Katie will catch up to Susan, the final distance traveled by Katie will be equal to the final distance traveled by Susan.
[tex] x_{f_{s}} = x_{0_{s}} + v_{0_{s}}t + \frac{1}{2}at^{2} [/tex]
[tex] x_{0_{k}} + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Since Susan gets a 45 minutes head start, in that time she traveled the following distance:
[tex] d = \frac{v}{t} = \frac{5 mi/h}{45 min*\frac{1 h}{60 min}} = 6.67 mi [/tex]
So, this will be the initial position of Susan.
[tex] 0 + v_{0_{k}}t = x_{0_{s}} + v_{0_{s}}t [/tex]
Hence, the time will be:
[tex] 5.2t = 6.67 + 5t [/tex]
[tex] t = 33.4 h [/tex]
Therefore, Katie will catch up to Susan after running 33.4 h.
I hope it helps you!
