Answer: 72.97 Minutes
Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.
To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.
Relative speed = Speed of car B - Speed of car A
Relative speed = 114 km/h - 77.0 km/h
Relative speed = 37.0 km/h
So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.
To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.
Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours
Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).
Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes
Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.
Hope this helps!