If we make a table out of this info, we would have rows being cyclist 1 and cyclist 2, with columns being distance, rate, and time. Working with cyclist 1. He is traveling at a rate of r. He meets cyclist 2 after 2 hours, so his time is 2. If distance = rate*time, then the distance he travels towards cyclist 2 is 2r. Now on to cyclist 2. His rate is 3 km per hour slower, so his rate is r-3. He meets cyclist 1 after 2 hours, so his time is also 2. If distance = rate*time, then the distance he travels towards cyclist 1 is 2(r-3). Because they are traveling towards each other on the same path and meet at a certain point, together they have traveled the whole 94 km. That means that the distance cyclist 1 travels + the distance that cyclist 2 travels = 94. The bolded equations are the distances that each cyclist traveled. We add them: [tex]2r+2(r-3)=94[/tex]. Using the distributive property, 2r + 2r - 6 = 94. And 4r = 100. r = 25. That means that cyclist 1 is traveling at a rate of 25 km per hour, and cyclist 2 is going 3 km per hour slower at 22 km per hour.
