Final answer:
To find the speed of the car when compared to a train that is 50% faster, we use the provided information on travel time and distance. By setting up and solving equations based on distance, speed, and time, we determine that the car's speed is 100 km/h.
Step-by-step explanation:
The student's question asks to find the speed of the car, given that a train can travel 50% faster than the car, both starting from point A and reaching point B 75 kilometers apart at the same time, with the train having lost 12.5 minutes due to stops.
Let the speed of the car be v km/h. Therefore, the speed of the train is 1.5v km/h. Since they both reach point B at the same time and the train lost 12.5 minutes, we can say that if the car takes t hours, the train takes t - 12.5/60 hours to travel 75 km (since 12.5 minutes is equal to 12.5/60 hours).
Using the equation distance = speed × time, we can set up two equations based on the information:
- Car: 75 = v × t
- Train: 75 = 1.5v × (t - 12.5/60)
From the first equation, t = 75/v. Substitute t in the second equation and solve for v to get the result. After solving, it's found that the car's speed is 100 km/h, which corresponds to option A.