To determine the distance a car will cover when traveling at a specific average speed over a given period of time, we use the formula:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Let's break down the steps with the given values:
1. Given Speed:
The car's average speed is [tex]\(\frac{200}{3} \text{ km/hr}\)[/tex].
2. Given Time:
The time duration is [tex]\(\frac{25}{2} \text{ hours}\)[/tex].
3. Calculating the Distance:
Using the formula, we substitute the values for speed and time:
[tex]\[
\text{Distance} = \left(\frac{200}{3}\right) \text{ km/hr} \times \left(\frac{25}{2}\right) \text{ hours}
\][/tex]
4. Multiplying the speed and time:
- First, we multiply the numerators together: [tex]\( 200 \times 25 = 5000 \)[/tex].
- Then, we multiply the denominators together: [tex]\( 3 \times 2 = 6 \)[/tex].
- Now, we have:
[tex]\[
\text{Distance} = \frac{5000}{6} \text{ km}
\][/tex]
5. Simplifying the Fraction:
- The fraction simplifies to its decimal form:
[tex]\[
\frac{5000}{6} = 833.3333333333334 \text{ km}
\][/tex]
Thus, the distance the car will cover in [tex]\(\frac{25}{2}\)[/tex] hours at an average speed of [tex]\(\frac{200}{3}\)[/tex] km/hr is [tex]\(833.3333333333334\)[/tex] km.
