Of course! Let's break down the problem step by step.
### Problem Statement
A car is moving at an average speed of [tex]\(\frac{200}{3} \text{ km/hr}\)[/tex]. We need to find out how much distance it will cover in [tex]\(\frac{15}{2} \text{ hours}\)[/tex].
### Step-by-Step Solution
1. Understand the given quantities:
- Speed of the car: [tex]\(\frac{200}{3} \text{ km/hr}\)[/tex]
- Time traveled: [tex]\(\frac{15}{2} \text{ hours}\)[/tex]
2. Use the formula for distance:
To find the distance covered, we can use the formula:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Distance} = \left(\frac{200}{3} \text{ km/hr}\right) \times \left(\frac{15}{2} \text{ hours}\right)
\][/tex]
4. Perform the multiplication:
To multiply these fractions, you multiply the numerators together and the denominators together:
[tex]\[
\text{Distance} = \frac{200 \times 15}{3 \times 2}
\][/tex]
5. Simplify the fraction:
[tex]\[
200 \times 15 = 3000
\][/tex]
[tex]\[
3 \times 2 = 6
\][/tex]
So,
[tex]\[
\text{Distance} = \frac{3000}{6}
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
\frac{3000}{6} = 500
\][/tex]
Thus, the car will cover a distance of [tex]\(500 \text{ kilometers}\)[/tex] in [tex]\(\frac{15}{2}\)[/tex] hours.
