Whenever the problem involves catching up or overtaking find the difference between their rates, and the distance that must be overcome.
Often the faster mover overcomes a head start by the slower. But even in that problem, the only important distance is the distance between them.
"A hiker walking at a constant rate of 4miles/hr is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles/hr. The cyclist stops to wait for the hiker 5 mins after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up? "
D=RT
What is the difference between their rates? 20 - 4 = 16 miles/hour
What is the distance that must be overcome? It's the difference in their rates (both are moving) in the formula. 16 * 5/60 = 16 * 1/12 = 16/12 = 4/3 mile.
How long will it take the hiker to cover 4/3 mile? Remember, the biker is still, the hiker moves at 4 mph. T = D/R = 4/3 / 4 = 1/3 hour = 20 minutes.
