Answer:
They meet in 2.22 hours.
Step-by-step explanation:
We can find the time at which Reagan and Nathan meet by equaling the time as follows:
[tex] v_{R} = \frac{x_{R}}{t} [/tex]
[tex] x_{R} = v_{R}t [/tex] (1)
[tex] v_{N} = \frac{x_{N}}{t} [/tex]
[tex] x_{N} = v_{N}t [/tex] (2)
Where R is for Reagan and N for Nathan.
Knowing that:
[tex] x_{R} + x_{N} = 40 mi [/tex]
By adding equations (1) and (2) we have:
[tex] x_{R} + x_{N} = v_{R}t + v_{N}t [/tex]
[tex] t = \frac{x_{R} + x_{N}}{|v_{R}| + |v_{N}|} = \frac{40 mi}{8 mi/h + 10 mi/h} = 2.22 h [/tex]
Therefore, they meet in 2.22 hours.
I hope it helps you!
