Answer:
The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.
Step-by-step explanation:
Let suppose that each hiker travels at constant speed, such that kinematic formulas are, respectively:
Hiker A
[tex]x_{A} = x_{A,o}+v_{A}\cdot t[/tex]
Hiker B
[tex]x_{B} = x_{B,o} +v_{B}\cdot t[/tex]
Relationship
[tex]v_{A} =- v_{B}-2.2\,mph[/tex] (They walk toward each other)
Where:
[tex]x_{A,o}[/tex], [tex]x_{A}[/tex] - Initial and final position of the hiker A, measured in miles.
[tex]x_{B,o}[/tex], [tex]x_{B}[/tex] - Initial and final position of the hiker B, measured in miles.
[tex]t[/tex] - Time, measured in hours.
[tex]v_{A}[/tex], [tex]v_{B}[/tex] - Velocities of hikers A and B, measured in miles per hour.
Given that [tex]x_{A,o} = 0\,mi[/tex], [tex]x_{B,o} = 22\,mi[/tex], [tex]x_{A} = x_{B}[/tex] and [tex]t = 5\,h[/tex], the system of equation is reduced to the following:
[tex]0\,mi -(v_{B}+2.2\,mph)\cdot (5\,h) = 22\,mi+v_{B}\cdot (5\,h)[/tex]
[tex]-5\cdot v_{B}-11 = 22+5\cdot v_{B}[/tex]
[tex]10\cdot v_{B} = -33[/tex]
[tex]v_{B} = -3.3\,mph[/tex]
Now, the velocity of the hiker A is:
[tex]v_{A} = - (-3.3\,mph)-2.2\,mph[/tex]
[tex]v_{A} = 1.1\,mph[/tex]
The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.
