The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.
let us assume the following;
x = rate of slower cyclist
x + 5 = rate of faster cyclist
We know that formula for distance is;
distance = travel time*rate
Thus;
2x + 2(x + 5) = 74
Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;
2x + 2x + 10 = 74
4x + 10 = 74
4x = 74 - 10
4x = 64
x = 64/4
x = 16
Rate of faster cyclist = 16 + 5 = 21 mph
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