Question

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?

Answer 1

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
Answer:
the rate of each cyclist is:
Cyclist A: v = 17mph
Cyclist B: v-10 = 7mhp