Question

Two hikers are 22 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other

Answer 1

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

$x_{A} = x_{A,o}+v_{A}\cdot t$

Hiker B

$x_{B} = x_{B,o} +v_{B}\cdot t$

Relationship

$v_{A} =- v_{B}-2.2\,mph$ (They walk toward each other)

Where:

$x_{A,o}$, $x_{A}$ - Initial and final position of the hiker A, measured in miles.

$x_{B,o}$, $x_{B}$ - Initial and final position of the hiker B, measured in miles.

$t$ - Time, measured in hours.

$v_{A}$, $v_{B}$ - Velocities of hikers A and B, measured in miles per hour.

Given that $x_{A,o} = 0\,mi$, $x_{B,o} = 22\,mi$, $x_{A} = x_{B}$ and $t = 5\,h$, the system of equation is reduced to the following:

$0\,mi -(v_{B}+2.2\,mph)\cdot (5\,h) = 22\,mi+v_{B}\cdot (5\,h)$

$-5\cdot v_{B}-11 = 22+5\cdot v_{B}$

$10\cdot v_{B} = -33$

$v_{B} = -3.3\,mph$

Now, the velocity of the hiker A is:

$v_{A} = - (-3.3\,mph)-2.2\,mph$

$v_{A} = 1.1\,mph$

The hikers A and B travel at rates of 1.1 miles per hour and 3.3 miles per hour, respectively.