A car travelling with 
5/7
 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

To solve this problem, we need to determine the actual speed of the car given that it covers 42 km in 1 hour 40 minutes and 48 seconds at \(\frac{5}{7}\) of its actual speed.

### Step 1: Convert the time to hours
First, let's convert the time to hours:

- 1 hour = 1 hour
- 40 minutes = \(\frac{40}{60} = \frac{2}{3}\) hours
- 48 seconds = \(\frac{48}{3600} = \frac{48}{3600} = \frac{2}{150} = \frac{1}{75}\) hours

Now, sum them up:

\[
\text{Total time in hours} = 1 + \frac{2}{3} + \frac{1}{75} 
\]

Convert \(\frac{2}{3}\) and \(\frac{1}{75}\) to decimals to add them more easily:

\[
\frac{2}{3} \approx 0.6667 \quad \text{and} \quad \frac{1}{75} \approx 0.0133
\]

So,

\[
\text{Total time} = 1 + 0.6667 + 0.0133 = 1.68 \text{ hours}
\]

### Step 2: Calculate the speed at \(\frac{5}{7}\) of the actual speed
The car covers 42 km in 1.68 hours at \(\frac{5}{7}\) of its actual speed.

So, the speed at \(\frac{5}{7}\) of its actual speed is:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{42 \text{ km}}{1.68 \text{ hours}} = 25 \text{ km/h}
\]

### Step 3: Find the actual speed
Let \(v\) be the actual speed of the car. Then,

\[
\frac{5}{7} \times v = 25 \text{ km/h}
\]

To find \(v\), multiply both sides by \(\frac{7}{5}\):

\[
v = 25 \times \frac{7}{5} = 35 \text{ km/h}
\]

### Final Answer
The actual speed of the car is **35 km/h**.

---

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Here are some related problems:

1. What is the time taken to cover 70 km at the actual speed of the car?
2. If the car traveled at \(\frac{3}{4}\) of its actual speed, how much time would it take to cover 42 km?
3. What would be the speed if the car covered 42 km in 2 hours?
4. How much distance would the car cover in 3 hours at its actual speed?
5. If the car's speed was reduced by 10 km/h, how long would it take to cover 42 km?
6. Find the actual speed if the car covers 60 km in 2 hours at \(\frac{4}{5}\) of its actual speed.
7. What would be the time difference if the car travels 42 km at the actual speed vs. \(\frac{6}{7}\) of the actual speed?
8. How long would it take for the car to cover 100 km at its actual speed?

**Tip:** When dealing with time in hours, minutes, and seconds, always convert everything to a single unit (like hours) for easier calculation.

Learn how to calculate the actual speed of a car that covers 42 km in 1 hour 40 minutes and 48 seconds at 5/7 of its actual speed. Step-by-step solution provided with conversion of time units and calculation of speed. Suitable for high school students and above.

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