Final answer:
The distance traveled by the car after the first minute is 5 meters, as determined by dividing the second minute's distance of 7.5 meters by the common ratio of 1.5.
Step-by-step explanation:
The student's question involves determining the distance traveled by a car after the first minute, assuming the car's movement follows a geometric progression. Given that the car travels distances of Ym, 7.5m, 11.25m, and 16.875m in the first, second, third, and fourth minutes respectively, it is clear that each term (distance covered in each minute) is a multiple of 1.5 times the previous term. In the second minute, the car travels 1.5 times the distance it did in the first minute (7.5m = 1.5 * Ym), so the distance traveled in the first minute (Ym) is 7.5m divided by 1.5.
Here is the step-by-step calculation to find Ym:
- Identify that from the second minute to the third, and the third minute to the fourth, the distances covered are in a consistent ratio (11.25m = 1.5 * 7.5m and 16.875m = 1.5 * 11.25m).
- Using this ratio, calculate the distance traveled in the first minute by dividing the distance traveled in the second minute by this common ratio (7.5m / 1.5).
- The distance the car traveled after the first minute is therefore 5 meters (Ym = 5m).