car is running at 5th of its actual speed covers a distance of 45 km in 2 hours 20 minutes find the actual speed

To find the actual speed of the car, let's break down the problem step by step:

1. **Convert Time to Hours**:
   - The time given is 2 hours and 20 minutes.
   - Convert 20 minutes to hours: \( \frac{20}{60} = \frac{1}{3} \) hours.
   - So, the total time taken is \( 2 + \frac{1}{3} = \frac{7}{3} \) hours.

2. **Calculate the Speed at 1/5th Actual Speed**:
   - The car covers 45 km in \( \frac{7}{3} \) hours.
   - The speed at 1/5th of its actual speed is:
     \[
     \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{45 \text{ km}}{\frac{7}{3} \text{ hours}} = \frac{45 \times 3}{7} = \frac{135}{7} \approx 19.29 \text{ km/h}
     \]

3. **Determine the Actual Speed**:
   - Since this speed is 1/5th of the actual speed, the actual speed \( S \) is:
     \[
     S = 19.29 \times 5 = 96.43 \text{ km/h}
     \]

So, the actual speed of the car is approximately **96.43 km/h**.

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you convert minutes into a fraction of an hour?
2. What is the formula for speed when distance and time are known?
3. How would the problem change if the car was running at 1/4th of its actual speed instead?
4. What are other units of speed, and how can you convert between them?
5. How can this method be used to find time if speed and distance are known?

**Tip:** Always make sure to convert all time units to the same format before performing any calculations.

Learn how to calculate the actual speed of a car when given the distance traveled and the time taken. This problem involves applying the speed formula to determine the speed at a fraction of the actual speed and then finding the actual speed based on the given parameters. Suitable for Grades 7-9.

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