The problem states that the length of a road is $380$ m, correct to the nearest $10$ m, and Jurita runs along this road at an average speed of $3.9$ m/s, correct to $1$ decimal place. The question asks to calculate the greatest possible time taken by Jurita.

1. Problem Description

The problem states that the length of a road is $380$ m, correct to the nearest $10$ m, and Jurita runs along this road at an average speed of $3.9$ m/s, correct to $1$ decimal place. The question asks to calculate the greatest possible time taken by Jurita.

2. Solution Steps

To find the greatest possible time, we need to consider the largest possible distance and the smallest possible speed.

The length of the road is $380$ m, correct to the nearest $10$ m. This means the actual length could be anywhere between $380 - 5 = 375$ m and $380 + 5 = 385$ m. Therefore, the largest possible distance is $385$ m.

The average speed is $3.9$ m/s, correct to $1$ decimal place. This means the actual speed could be anywhere between $3.9 - 0.05 = 3.85$ m/s and $3.9 + 0.05 = 3.95$ m/s. Therefore, the smallest possible speed is $3.85$ m/s.

We know that

$Time = \frac{Distance}{Speed}$.

So, the greatest possible time is $\frac{385}{3.85}$.

$Time = \frac{385}{3.85} = \frac{38500}{385} = 100$ seconds.

3. Final Answer

The greatest possible time taken by Jurita is 100 seconds.