Aaron starts walking at a rate of 3 mi/h on a road toward a store 10 mi away. zhang leaves the store when aaron starts walking, and he walks toward aaron along the same road at 2 mi/h. how many hours will pass before they meet?

The first thing you should do is write the equation of the position for each person. After having them you must match them because they will be in the same position when they are at a point. After equalizing you clear the time. Attached solution.
The solution is t=2 hours.

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facundo3141592 facundo3141592 · Answer 2 · 2021-10-15T16:12:11+02:00

We want to find how much time will pass before Aaron and Zhang meet, given that they are walking in opposite directions along the same road.

The answer is:

They will meet after two hours.

To find this, we need to get the position equations for each one.

We also need to remember the general relation:

distance = speed*time.

Let's also define the zero in the position as Aaron initial position.

Then Aaron equation is written as:

[tex]P_A(t) = (3mi/h)*t[/tex]

Where t is time in hours.

Zhang starts at the store, so his initial position is 10 mi, and he walks at a speed of 2 miles per hour in the opposite direction as Aaron, then his equation is:

[tex]P_Z(t) = 10mi - (2mi/h)*t[/tex]

They will meet when:

[tex]P_A(t) = P_Z(t)[/tex]

So we just need to solve:

[tex](3mi/h)*t = 10mi - (2mi/h)*t\\\\(3mi/h)*t + (2mi/h)*t = 10mi\\\\(5mi/h)*t = 10mi\\\\t = (10 mi)/(5 mi/h) = 2 h[/tex]

They will meet after two hours

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