from the grid on Diane's swim you can see that, for every two squares on the grid over the x-axis, it goes up 3 squares over the y-axis, it moves 2 to the right and then 3 up, and you get the next point. What does that mean? well, is a constant speed and thus the graph is a line, with a slope of 3 meters per 2 seconds, so her slope is 3/2 m/s.
now, for Rick's slope, we can just pick two points off of it, say, hmmm 10, 12.5 and 20, 25, and get the slope,
![\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 10}} &,&{{ 12.5}}~) % (c,d) &&(~{{ 20}} &,&{{ 25}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{25-12.5}{20-10}\implies \cfrac{12.5}{10}\implies \cfrac{(125)/(10)}{10} \\\\\\ \cfrac{(125)/(10)}{(10)/(1)}\implies \cfrac{125}{10}\cdot \cfrac{1}{10}\implies \cfrac{125}{100}\implies \cfrac{5}{4}\cdot \cfrac{meters}{second}]()
so Diane is doing 3 meters for every 2 seconds, and Rick is doing 5 meters for every 4 seconds.
how long will it be for each to do the 150 meters anyway?


what's their difference? well y - x.