Solving Systems by Graphing

Will the Women Ever Catch the Men?

*Examining data from the past can predict the future if you know how to
SOLVE A SYSTEM BY GRAPHING!

Here's the situation: women and men have been running the 800 meter race in the Olympics for a long time. In the last 50 years, the trend has been for faster and faster times, but it appears that the women are getting faster, FASTER.

Will they ever catch the men? Will they ever run FASTER than the men? Mathematics can give us an answer. Follow the steps below to see what might happen.

Here's the data you will need:
*the scores below are approximate

year	women's best time in seconds
1952	124
1956	122
1960	121
1964	118
1968	114
1972	115
1976	117
1980	116
1984	115
1988	115
1992	112
1996	112
2000	111

year	men's best time in seconds
1952	109
1956	109
1960	107
1964	106
1968	105
1972	104
1976	106
1980	105
1984	105
1988	104
1992	104
1996	104
2000	103

Step 1: Find a piece of graph paper about 30 blocks wide and 40 blocks long, and turn it horizontally, so that the longer side is at the bottom.

Step 2:

Title your graph "Men's and Women's Best Olympic Times for the 800 Meter Race."
Label the "x" axis (Year) and start it at 1952 with each block representing 4 years. This will make every line an Olympic year. The graph should make it to about the year 2100 when labeled like this.
Label the "y" axis (Time in Seconds). Start it at 80 seconds and let every block represent 2 seconds. Your graph should make it to at least 130 seconds when labeled like this.

Step 3: Now graph the data in the tables above using dots for the women's data and small squares for the men's data.

*(Be sure to put a key on the graph indicating what these dots and squares represent.)

Step 4: Draw a line of "best fit" for the women's data and one for the men's data.

Step 5: You should notice that the women's line is sloping downward a bit more steeply, and this causes the lines to intersect. The spot where they intersect is the year and the time that the women will catch the men. Write its coordinates here:

(_______ , _______)

click HERE to see an example.