Answer:
slower cyclist = 14 mph
faster cyclist = 22 mph
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Work Shown:
x = rate of slower cyclist
x+8 = rate of faster cyclist, since this person travels 8 mph faster
After 4 hours, the slower cyclist covers 4x miles while the faster cyclist covers 4(x+8) = 4x+32 miles. In total, they cover 4x+4x+32 = 8x+32 miles. In other words, this is the distance between them after 4 hours.
Set this equal to 144 and solve
8x+32 = 144
8x = 144-32
8x = 112
x = 112/8
x = 14 is the slower cyclist's speed in mph
x+8 = 14+8 = 22 is the faster cyclist's speed in mph
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as a check:
distance = rate*time = 4*14 = 56 miles is covered by the slower cyclist
d = r*t = 4*22 = 88 miles is covered by the faster cyclist
56+88 = 144 miles is the total distance between the two cyclists after 4 hrs
the answers are confirmed