Final answer:
The average speed of the car is 106 km/h, and it takes 2.5 hours to travel 265 km. The train travels at an average speed of 126 km/h.
Step-by-step explanation:
To find the average speed of the car and the time taken to travel 265 km, we can use the relationship between distance, speed, and time, which is expressed as speed = distance/time.
Let V be the average speed of the car. Then, the average speed of the train will be V + 20 km/h. Since both travel the same time (t), we can set up the following equations:
- Speed of car: V
- Speed of train: V + 20 km/h
- Distance traveled by car: 265 km
- Distance traveled by train: 315 km
Therefore, we can write two equations based on the definition of speed:
- 265 km = V * t
- 315 km = (V + 20) * t
Next, we can solve these equations simultaneously. Divide the distance by the speed for each vehicle to find the time:
- t = 265 km / V
- t = 315 km / (V + 20)
Since the time t is the same for both, we can equate these two expressions:
265 / V = 315 / (V + 20)
Now we cross-multiply:
265 * (V + 20) = 315 * V
265V + 5300 = 315V
50V = 5300
V = 5300 / 50
V = 106 km/h
This is the average speed of the car. The train, therefore, travels at 106 + 20 = 126 km/h.
To find the time, use the speed of the car:
t = 265 km / 106 km/h = 2.5 hours
This is the time taken to travel 265 km by car.