Question 263249
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?
----
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
===============================================================
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)
===============================
Cheers,
Stan H.