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### Problem Transcription:
- **Context**: Marvin is going to visit his friend Coco who is suffering from a fever. Marvin uses his car to travel to Coco's house. The initial speed of Marvin's car is 48 km/h, then he continuously increases one-fourth of his previous speed.

1. **Question 1**: Marvin accelerates every minute by increasing his speed by one-fourth of the previous value. If the journey lasts for 10 minutes, what will be the speed of his car for every minute?

2. **Question 2**: Given that Marvin is always increasing his speed, what is the total distance he has covered after 10 minutes of driving?

3. **Question 3**: What is the increase in speed experienced by the car after each minute interval? Relate your answer to the table below.

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### Solving the problem:

#### 1. Speed at each minute:
The initial speed is given as 48 km/h, and Marvin increases his speed by one-fourth of the previous value each minute. This is a geometric progression where each term is \(\frac{5}{4}\) times the previous one.

- At \(t = 0\), speed \(S_0 = 48\) km/h.
- At \(t = 1\), speed \(S_1 = 48 \times \frac{5}{4} = 60\) km/h.
- At \(t = 2\), speed \(S_2 = 60 \times \frac{5}{4} = 75\) km/h.
- At \(t = 3\), speed \(S_3 = 75 \times \frac{5}{4} = 93.75\) km/h.
- Continue this pattern until \(t = 10\).

#### 2. Total distance covered in 10 minutes:
Since the speed increases geometrically, we calculate the distance covered in each minute and sum them. The formula for distance in each minute is:

\[
d = \text{speed in km/h} \times \frac{1}{60} \, \text{(since 1 minute is \(\frac{1}{60}\) of an hour)}.
\]

We can calculate the total distance by adding the distances covered at each minute.

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Would you like to continue solving the problem with more detail or need clarification on any part? Let me know!

Here are 5 related questions you can explore:

1. How do you calculate the speed after 5 minutes of acceleration?
2. What is the formula for the sum of a geometric progression, and how can it apply here?
3. How would the problem change if Marvin increased his speed by a fixed amount instead of a fraction?
4. What if Marvin started at a different speed—how would this affect the solution?
5. Can this scenario be modeled using calculus, and how would that work?

**Tip**: In problems with increasing speed or rates, geometric progression is a powerful tool to simplify calculations.

Marvin is going to visit his friend Coco who is suffering from a fever. Marvin uses his car to travel to Coco's house. The initial speed of Marvin's car is 48 km/h, then he continuously increases one-fourth of his previous speed. Calculate the speed of his car for every minute if the journey lasts for 10 minutes, the total distance covered, and the increase in speed after each minute.

Explore how to calculate increasing speeds using geometric progression with an initial speed of 48 km/h and a consistent increase of one-fourth every minute. This detailed guide includes formulas for speed and distance over a 10-minute journey.

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