Motion Problems - Worked Out Solutions

 

1. Tonya and Freda drive away from Norfolk on the same road in the same direction. If Tonya is averaging 52 mph and Freda is averaging 65 mph, how long will it take for them to be 39 miles apart?

  1. Read the problem. Guess.

Before you guess you should ask yourself how much distance will be between them after one hour.

  1. Define x, usually to answer the question.
  2. Define other unknown quantities in terms of x.

We can accomplish both of the above steps with the following table.

 

      Rate

       Time
Distance

Tonya

52
x

52x

Freda

65

x

65x
  1. Form the equation.

Now that we have algebraic names for the distances, the equation will depend on whether Tonya and Freda are traveling in the same direction or in opposite directions. Since they are traveling in the same direction we want the difference of their distances to be 39 miles. The equation will be 65x – 52x = 39.

  1. Solve the equation.

65x – 52x = 39

          13x = 39

              x = 3 hours.

  1. Answer the question.

It will take 3 hours for them to be 39 miles apart. (That’s 13 miles each hour.)

 

 

2. Tonya and Freda drive away from Norfolk on the same road in opposite directions. If Tonya is averaging 52 mph and Freda is averaging 65 mph, how long will it take for them to be 39 miles apart? Round your answer to the nearest minute.

  1. Read the problem. Guess.

Now that they are traveling in opposite directions, how far apart will they be after one hour?

  1. Define x, usually to answer the question.
  2. Define other unknown quantities in terms of x.

     

 

Rate
Time
Distance

Tonya

52

x

52x

Freda

65

x

65x
  1. Form the equation.
Since they are traveling in opposite directions, 65x + 52x = 39
  1. Solve the equation.

52x + 65x = 39

         117x = 39

              x  = 1/3 hour

  1. Answer the question.

One third of an hour is twenty minutes.

 

 

 

3. Bernadette drove 120 miles. The first part of the trip she averaged 60 mph, but on the second part of the trip she ran into some congestion and averaged 48 mph. If the total driving time was 2.2 hours, how much time did she spend at 60 mph?

  1. Read the problem. Guess.
  2. Define x, usually to answer the question.
  3. Define other unknown quantities in terms of x.

     

 

Rate
Time
Distance

First part

60

x

60x

Second part

48

2.2 – x

48(2.2 – x)
  1. Form the equation.

Now that we have nice algebraic names for the distances, what do we know about these distances? They total to be 120 miles. So 60x + 48(2.2 – x) = 120.

e.   Solve the equation.

60x + 48(2.2 – x) = 120

60x + 105.6 – 48x = 120

                       12x = 14.4

                           x = 1.2 hours

f.     Answer the question.

Since x was defined to answer the question, we are done. She spent 1.2 hours at 60 mph.

 

 

 

 

 

 

 

 

 

 

 

4. Dr. John left New Orleans at 12 noon. His drummer left at 1:00 traveling 9 mph faster. If the drummer passed Dr. John at 6:00, what was the average speed of each?

  1. Read the question. Guess.
  2. Define x, usually to answer the question.
  3. Define other unknown quantities in terms of x.

     

 

Rate
Time
Distance
Dr. John

x

6

6x

Drummer

x + 9

5

5(x + 9)
  1. Form the equation.

Since the drummer catches him, their distances should be equal. 6x = 5(x + 9).

e.   Solve the equation.

6x = 5(x + 9)

6x = 5x + 45

  x = 45 mph

f.     Answer the question.

Dr. John was averaging 45 mph and the drummer was averaging x + 9 = 54 mph.

 

           x = 1.5 hours

Math 03 Problem-Solving Menu
Virtual Math Lab Menu
Disclaimer TCC Home
Created by: Marcia Tharp
Revised on: 10.14.02 by Dr. Marcia Tharp
Send comments to: mtharp@tcc.edu or rgill@tcc.edu