Use the following information to complete parts 1, 2, and 3 of this problem.

v  Jose, Mario, and Melanie went on a weeklong cycling trip.

v  The distances each person traveled for the first 3 hours are listed below.

v  The times reflect only the actual biking, not any resting time.

Cycling time (hours) / Distance traveled (miles)
Jose / Mario / Melanie / Mike
0 / 0 / 0 / 0 / 0
1 / 5 / 7 / 9
2 / 10 / 14 / 18
3 / 15 / 21 / 27
4
5
6
7
8
9
10

Part 1:

A. How fast did each person travel for the first 3 hours? (hint: miles per hour)

Jose: _____ Mario: _____ Melanie: _____

Explain how you got your answers (what did you do?): ______

B. Complete the table above assuming each person continued traveling at the same rate.

C. How far had each person traveled after 7 hours?

Jose: _____ Mario: _____ Melanie: _____

Part 2:

A. Graph the time (x) and distance (y) data for Jose, Mario, and Melanie on the same graph.

- Be sure to label each line by name

1 2 3 4 5 6 7 8 9 10

Time traveled (hours)

B. Use the graph to find the distance each person traveled in 6½ hours.

Jose: _____ Mario: _____ Melanie: _____

C. Use the graph to find the time it took each person to travel 70 miles.

Jose: _____ Mario: _____ Melanie: _____

D. How does each rider’s speed (rate) affect their graph? ______

3. Write an equation (direct variation equation) for each rider that can be used to calculate the distance traveled (y) after a given number of hours (x).

Jose: ______Mario: ______Melanie: ______

4. Mike was on the bike trip with Jose, Mario, and Melanie. The table below describes the distances he traveled during day 1 of his trip.

Time (hours) / Distance (miles)
0 / 0
1 / 6.5
2 / 13
3 / 19.5
4 / 26
5 / 32.5
6 / 39

A. Write an equation for the distance (y) Mike travels after x hours.

(Hint – use a direct variation).

Mike: ______

B. Add Mike’s information to the table with the other riders, and complete the missing information.

C. Graph Mike’s information on the same graph as the other riders.

Be sure to label it!

D. Find the following distances that Mike traveled in the given time.

Answer: Check the method used to find your answer:

7 hours: _____ table_____ graph_____ equation_____

9½ hours: _____ table_____ graph_____ equation_____

E. Find the amount of time it will take Mike to travel the given distances.

Answer: Check the method used to find your answer:

100 miles: _____ table_____ graph_____ equation_____

237 miles: _____ table_____ graph_____ equation_____

F. List one advantage and one disadvantage of using each form of representation (table, graph, equation).

Type of representation / Advantage / Disadvantage
Table
Graph
Equation

G. In part 1-A you found the speed/rate for Jose, Mario, and Melanie. Find Mike’s speed (miles per hour).

Mike:_____

E. Now the speed for all 4 riders à Jose, Mario, Melanie, and Mike.

Who rides the fastest? _____ How do you know?_____

Who rides the slowest? _____ How do you know? _____