a cyclist leaves his training base for a morning workout rid

a cyclist leaves his training base for a morning workout riding at a rate of 18mph.
one hour later, his support staff leaves the base in a car going 45mph in the same direction.
how long will it take the support staff to catch up with the cyclist?

Solution

Cyclist DATA:
rate = 18 mph ; time = x hrs ; distance = rt = 18x miles
-------------------------
Staff DATA:
rate = 45 mph ; time = x-1 hrs ; distance = rt = 45(x-1) miles
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Equation:
cyclist distance = staff distance
18x = 45(x-1)
18x = 45x - 45
27x = 45
x = 5/3 hr (cyclist time)
x-1 = 2/3 hr (staff time)