Two cyclists start at the same point and travel in opposite directions. one cyclist travels 10 /mi h slower than the other. if the two cyclists are 96mi apart after 4 hours, what is the rate of each cyclist?

We write the cinematic equation for each cyclist.
 We have then:
 Cyclist A:
 ra = v * t
 Cyclist B:
 rb = - (v-10) * t
 After 4 hours we have:
 ra-rb = 4v - (-4 (v-10))
 96 = 4v - (-4 (v-10))
 Rewriting:
 96 = 4v + 4 (v-10)
 96 = 4v + 4v - 40
 96 = 8v - 40
 v = (96 + 40) / (8)
 v = 17 mph
 Cyclist A: v = 17mph
 Cyclist B: v-10 = 17-10 = 7mhp
 
 the rate of each cyclist is:
 Cyclist A: v = 17mph
 Cyclist B: v-10 = 7mhp

Ais the answer for your question