car is running at 5/7 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 first break down the problem.

### Step 1: Convert the time into hours.
2 hours 20 minutes is equivalent to:
\[
2 \text{ hours} + \frac{20}{60} \text{ hours} = 2 + \frac{1}{3} = \frac{7}{3} \text{ hours}
\]

### Step 2: Calculate the speed at the reduced speed.
The car covers 45 km in \(\frac{7}{3}\) hours at \(\frac{5}{7}\) of its actual speed. So, the speed at this reduced rate is:
\[
\text{Reduced speed} = \frac{\text{Distance}}{\text{Time}} = \frac{45 \text{ km}}{\frac{7}{3} \text{ hours}} = \frac{45 \times 3}{7} = \frac{135}{7} \text{ km/h}
\]

### Step 3: Find the actual speed.
Let the actual speed be \( x \). Since the car is running at \(\frac{5}{7}\) of its actual speed, we have:
\[
\frac{5}{7} \times x = \frac{135}{7}
\]
To find \( x \), multiply both sides by \(\frac{7}{5}\):
\[
x = \frac{135}{7} \times \frac{7}{5} = \frac{135}{5} = 27 \text{ km/h}
\]

### Final Answer:
The actual speed of the car is **27 km/h**.

Would you like more details or have any questions? 

Here are some related questions:
1. If the car was running at its actual speed, how long would it take to cover 45 km?
2. What distance would the car cover in 1 hour at its reduced speed?
3. If the car runs at 3/4 of its actual speed, how much time will it take to cover 27 km?
4. What is the ratio of the time taken at reduced speed to the time taken at actual speed for the same distance?
5. How much time is saved by running at the actual speed instead of the reduced speed over 90 km?

**Tip:** When dealing with problems involving time and speed, converting all units to the same base (like hours) at the start simplifies calculations.

Learn how to find the actual speed of a car that covers 45 km in 2 hours 20 minutes while running at 5/7 of its actual speed. Detailed step-by-step solution provided, including calculations and conversions of time and speed.

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