Answer to Question #234219 in Physics for Lean Quiap

Question

Two cyclist race against a clock in a 50-km cross-country route. Cyclist A travels at a constant velocity of 30 km/h. Cyclist B started 10.0 minutes after cyclist A, however cyclist B manages to catch up with cyclist A at the finish line. What is the speed of cyclist B assuming his speed is constant?

Answer 1

Find the time required for the first cyclist to pass the course:

$$t=\frac{50}{30}=\frac53\text{ h}.$$

The time for the second cyclist is 10 minutes (1/6 hours) shorter:

$$\tau=t-\frac16=\frac32\text{ h}.$$

Therefore, the speed of the second cyclist is

$$v=\frac{50}{3/2}=33.3\text{ km/h}.$$