the cyclist going at a constant rate of 18 miles per hour is passed by a motor-cyclist traveling in the same direction along the same path at 48 miles per hour. the motor-cyclist stops to wait for the cyclist 15 minutes after passing cyclist, while the cyclist continues to travel at constant rate, how many minutes must the motor-cyclist wait until the cyclist catches up?  Choose the correct choice: A) 25 B) 30 C) 35 D) 40 E) 45

Rationale: for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )
Answer: A