Question

A car is speeding at 60 miles per hour along a winding coastal highway. The posted speed limit is 45 miles per hour. A police officer begins to chase the car 5 minutes after the speeding car passes. The police officer travels at a rate of 75 miles per hour

Answer 1

Let the police car catch up with the car speeding at 60 miles per hour in x minutes. In x minutes, I.e. in x/60 hour, the first car(speeding at 60 miles per hour) will travel a distance of 60* x/60 = x miles.

The police officer begins to chase the car 5 minutes after the speeding car passes. In x-5 minutes, the police officer will travel 75(x-5)/60 miles = (5x/4)- 25/4 miles. Thus, if the police car catches up with the car speeding at 60 miles per hour in x minutes, then x =(5x/4)- 25/4 or, 5x/4 – x = 25 or, x/4 = 25 so that x = 4*25 = 100.

Hence, the police car will catch up with the car speeding at 60 miles per hour in 100minutes or, 1 hour, 40 minutes.