Question

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Answer 1

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:  $2r+2(r-3)=94$.  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.