One way to understand a problem in order to analyze it is to create a table or a graph.

Example: Natalie and Anna are training for the Houston Marathon. Natalie can run six miles per hour, and Anna can run eight miles per hour. After 1 1 2 hours, how far have Natalie and Anna traveled?

Source: Euthman/Flickr

There are many ways to solve this problem. A picture or model can be created to visualize the distance Natalie and Anna run in an hour.

From the picture, you can see that after one hour, Natalie runs six miles, and Anna runs eight miles.

Fill in the blanks.

• In two hours Natalie can run Interactive button. Assistance may be required. _____ 12 miles and Anna can run Interactive button. Assistance may be required. _____ 16 miles.
• To find out how far they can run in 1 1 2 hours, we can look at the model half way between the Interactive button. Assistance may be required. _____ one hour and Interactive button. Assistance may be required. _____ two hour mark.

• In 1 1 2 hours, Natalie can run Interactive button. Assistance may be required. _____ 9 miles and Anna can run Interactive button. Assistance may be required. _____ 12 miles.

Anna will complete the marathon faster than Natalie because Anna is running at a faster rate.

This information can be written in a table. Click on the blanks to check your answer.

Since Natalie runs at a speed of Interactive button. Assistance may be required. _____ 6 miles per hour, her distance can be calculated by multiplying her rate of Interactive button. Assistance may be required. _____ speed by the time. Example: 3 hours × 6 mph ⇒ 3 × 6 = 18 miles.

• In 4 hours if Natalie runs at a consistent rate she could run Interactive button. Assistance may be required. _____ 24 miles .
• In 2 1 2 hours, she could run Interactive button. Assistance may be required. _____ 15 miles .
• In Interactive button. Assistance may be required. _____, 5 hours Natalie could run 30 miles.
• In order to find out how long it would take Natalie to run the Interactive button. Assistance may be required. _____ 26 mile marathon an equation is needed.
• The equation is Interactive button. Assistance may be required. _____ y = 6x where y is the distance traveled and x is the number of hours run.
• Substitute. Interactive button. Assistance may be required. _____ 26 in for the number of miles, Interactive button. Assistance may be required. _____ y .
• Solve for x: Interactive button. Assistance may be required. _____ y = 6x
  26 = 6x
  4 1 3 = x 1 3 = x 1 3 = x .
• One-third of an hour is Interactive button. Assistance may be required. _____ 20 minutes.
• It would take Natalie Interactive button. Assistance may be required. _____ 4 hours and 20 minutes to finish the 26 mile marathon.
• In 4 hours if Anna ran at a constant rate she would run Interactive button. Assistance may be required. _____ 32 miles .
• In 3 hours, she would run Interactive button. Assistance may be required. _____ 24 miles .
• In 2 1 2 hours, she would run Interactive button. Assistance may be required. _____ 20 miles .
• In Interactive button. Assistance may be required. _____, 5 hours Anna could run 40 miles.
• In order to find out how long it would take Anna to run the Interactive button. Assistance may be required. _____ 26 mile marathon, an equation is needed.
• The equation is Interactive button. Assistance may be required. _____ y = 8x where y is the distance traveled and x is the number of hours run.
• Substitute Interactive button. Assistance may be required. _____ 26 in for the number of miles, Interactive button. Assistance may be required. _____ y .
• Solve for x: Interactive button. Assistance may be required. _____ y = 8x
  26 = 8x
  3 1 4 = x
• One-fourth of an hour is Interactive button. Assistance may be required. _____ 15 minutes.
• It would take Anna Interactive button. Assistance may be required. _____ 3 hours and 15 minutes to finish the 26 mile marathon.
• If Natalie and Anna start the marathon at 8 A.M., Natalie would finish the marathon at Interactive button. Assistance may be required. _____ 12:20 P.M and Anna would finish the marathon at Interactive button. Assistance may be required. _____ 11:15 A.M .

Source: Michael Wimpee/Flickr

Example: Anna and Natalie have to arrive to check in for the marathon at 7 A.M. in order to have enough time walk to the start line. After the marathon, it will take 30 minutes to walk from the finish line back to their car. The convention center parking lot charges $5 per hour or part of an hour to park. Should Anna and Natalie carpool and split the parking fees or is it cheaper for Anna to take her own car and leave when she finishes the race?

• If Natalie and Anna started the race at 8 A.M., then Natalie would finish the marathon at Interactive button. Assistance may be required. _____ 12:20 P.M and Anna would finish the marathon at Interactive button. Assistance may be required. _____ 11:15 A.M .
• If Anna takes her own car, it will be in the parking lot Interactive button. Assistance may be required. _____ 1 hour before the marathon starts.
• Anna will finish the marathon in Interactive button. Assistance may be required. _____ 3 hours and Interactive button. Assistance may be required. _____ 15 minutes.
• Anna will return to the parking lot at Interactive button. Assistance may be required. _____ 11:15 AM .
• To find the total number of hours Anna's car would be parked, subtract Interactive button. Assistance may be required. _____ 11:15 A.M. from Interactive button. Assistance may be required. _____ 11:45 A.M. .
• Anna's car would be parked Interactive button. Assistance may be required. _____ 4 hours and Interactive button. Assistance may be required. _____ 45 minutes.
• Since the convention parking lot charges $5 for all or part of an hour, Anna will be charged for Interactive button. Assistance may be required. _____ 4 hours and Interactive button. Assistance may be required. _____ 45 minutes.
• Anna would be charged Interactive button. Assistance may be required. _____ $25 to park in the convention parking lot if she did NOT carpool.
• Natalie would finish the race at Interactive button. Assistance may be required. _____ 12:20 P.M. .
• Natalie would return to the parking lot at Interactive button. Assistance may be required. _____ 12:50 P.M. .
• It would be approximately Interactive button. Assistance may be required. _____ 1 hour later than Anna's return to the parking lot.
• If Anna and Natalie carpooled to the marathon, they would be charged Interactive button. Assistance may be required. _____ $5 more than Anna driving alone or Interactive button. Assistance may be required. _____ $30 .
• Since they would split the cost, Anna would pay Interactive button. Assistance may be required. _____ $15 to park.
• Anna and Natalie Interactive button. Assistance may be required. _____ should carpool to the marathon because it is cheaper.