A car travelling at 60km/h overtake another car travelling at 42km/h. Assuming each to be 5m long , find the time taken during the overtake and the total road d

Question

A car travelling at 60km/h overtake another car travelling at 42km/h. Assuming each to be 5m long , find the time taken during the overtake and the total road distance used for overtake?

Answer 1

First if we need to understand what they mean by over take.  If this means the cars are already front bumper to front bumper or if the faster car is actually behind the slower car.  Because we are given the lengths of both cars, I am assuming that the faster car is behind the slower car and the front bumper of the fast car is even with the back bumper of the slower car.   

 ----------------Fast car (5m)

                     ----------------slower car (5m)

 

Next, we need to determine how much faster the fast car is traveling.  

60 km/h - 42 km/h = 18 km/h = 18 km/60 min = 18,000 m/60 min = 300 m/1 min = 300 m/60 sec and simplifies to 5 m/ 1 sec.  Therefore, the faster car can gain 5 m every sec.  So, it will take 1 sec to be side by side and another second to be directly ahead of the slower car.  I would consider this 2 seconds to over take the slower car.  

 

Now, we need to answer the second part of the question and remember that the faster car has traveled the most distance and we need to determine the total distance it took to over take the car.  So, it has been traveling at 60 km/h for two seconds.  

60 km/h = 60 km/60 min = 1 km/1 min = 1,000 m/60 sec = 16.66 m/1 sec

Since it took two seconds, the faster car would have traveled 33.33 m in the two seconds it took to overtake the other car.

 

On the other hand, if we assume that the cars were front bumper to front bumper to begin, we would only need to travel 5m. This would have taken only 1 second, and the total distance traveled would have been 16.66 meters.