Solving a Motion Problem (2.8.1)

Question 1

• Process for solving word problems:
• Define the variable.
• Write what facts you know.
• Create the equation.
• Solve the equation.
• Check your answer.

Answer 1

• Process for solving word problems:
• Define the variable.
• Write what facts you know.
• Create the equation.
• Solve the equation.
• Check your answer.

Question 2

• This type of motion problem relates an average speed (or rate) to the distance and time.

Answer 2

• This type of motion problem relates an average speed (or rate) to the distance and time.

Question 3

The first thing to do, always, is to read the problem to see
what you are looking for and what you know.

In this problem, you are asked how long did the student
travel? Your variable, t, will be defined as the student’s travel time during the second leg of the trip.

You know two distance facts and something about two rates. The rate during the first leg of the trip is defined with variable r.

You know that you will likely use the tried and true formula connecting distance, speed (rate), and time.

This much information allows you to set up two equations, one for each leg of the trip.

You want to eliminate one variable, if possible, so you can solve the equation.

The equation for the first leg of the trip can be solved for r. Then, substitute that expression for r into the equation for the second leg of the trip.

Now solve for t.

You find that t = –9/2 or 2. However, you eliminate the
negative answer because time cannot be negative.

So, you know that t = 2 hrs. And that gives you the time for the second leg of the trip.

Since the first leg of the trip was defined to be t + 1, that
means it took 3 hours. Therefore, the total time required for the student’s trip was 2 hours + 3 hours, or 5 hours.

Answer 3

The first thing to do, always, is to read the problem to see
what you are looking for and what you know.

In this problem, you are asked how long did the student
travel? Your variable, t, will be defined as the student’s travel time during the second leg of the trip.

You know two distance facts and something about two rates. The rate during the first leg of the trip is defined with variable r.

You know that you will likely use the tried and true formula connecting distance, speed (rate), and time.

This much information allows you to set up two equations, one for each leg of the trip.

You want to eliminate one variable, if possible, so you can solve the equation.

The equation for the first leg of the trip can be solved for r. Then, substitute that expression for r into the equation for the second leg of the trip.

Now solve for t.

You find that t = –9/2 or 2. However, you eliminate the
negative answer because time cannot be negative.

So, you know that t = 2 hrs. And that gives you the time for the second leg of the trip.

Since the first leg of the trip was defined to be t + 1, that
means it took 3 hours. Therefore, the total time required for the student’s trip was 2 hours + 3 hours, or 5 hours.