Scenario:

There is a hiking trail near the town where Han and Jada live that starts at a parking lot and ends at a lake. Han and Jada both decide to hike from the parking lot to the lake and back, but they start their hikes at different times.
At the time that Han reaches the lake and starts to turn back, Jada is 0.6 miles away from the parking lot and hiking at a constant speed of 3.2 miles per hour toward the lake. Han’s distance, dd, from the parking lot can be expressed as d = − 2.4 t + 4.8, where tt represents the time in hours since he left the lake.

What is an equation for Jada’s distance from the parking lot as she heads toward the lake?

Han and Jada both decide to hike from the parking lot to the lake and back, but they start their hikes at different times.
At the time that Han reaches the lake and starts to turn back, Jada is 0.6 miles away from the parking lot.
Jade is hiking at a constant speed of 3.2 miles per hour toward the lake.
Han’s distance, d, from the parking lot can be expressed as d = − 2.4 t + 4.8, where t represents the time in hours since he left the lake.

Solution

Statement 1

Han and Jada both decide to hike from the parking lot to the lake and back, but they start their hikes at different times.

As both are starting at different timings, therefore, both are independent of each other.

Statement 4,

as given to us Han’s distance, d, from the parking lot can be expressed as d = − 2.4 t + 4.8,

So, when Han started the time would be t=0, substituting the value,

[tex]d = -2.4 t + 4.8\\ d= -2.4(0)+4.8\\ d=4.8[/tex]

Therefore, when Han begins the journey his distance from the park is 4.8 miles. thus, the distance between the lake and the park is 4.8 miles.

Statement 2,

At the time that Han reaches the lake and starts to turn back, Jada is 0.6 miles away from the parking lot

We know,

distance = speed x time
distance covered by Jade = 3.2 miles/hour x t

Now, the total distance between the lake and the parking is 4.8 miles, so as time goes on, Jade will cover more distance, therefore, reducing the distance between him and the parking.

distance between Jade and parking

= distance between the lake and the park - distance between jade and the parking

d = 4.8 - 3.2t

Hence, the equation for Jada’s distance from the parking lot as she heads toward the lake is d = 4.8 - 3.2t.

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