A car travelling with `(5)/(7)` of its usual speed covers 42 km in 1 hour 40 min 48 sec. What is the usual speed of the car?

Answer

To find the usual speed of the car, we will follow these steps:

### Step 1: Convert the time taken into hours
The car covers a distance of 42 km in 1 hour, 40 minutes, and 48 seconds. We need to convert this entire time into hours.

1 hour = 60 minutes = 3600 seconds
40 minutes = 40 × 60 = 2400 seconds
48 seconds = 48 seconds

Total time in seconds = 3600 + 2400 + 48 = 6048 seconds
Now, convert seconds into hours:
Total time in hours = 6048 seconds ÷ 3600 seconds/hour = 1.68 hours

### Step 2: Set up the equation for speed
Let the usual speed of the car be \( x \) km/h. The car is travelling at \( \frac{5}{7} \) of its usual speed. Therefore, the speed of the car during the journey is:
Speed = \( \frac{5}{7} x \) km/h

### Step 3: Use the formula for speed
We know that speed = distance/time. We can set up the equation:
\[ \frac{5}{7} x = \frac{42 \text{ km}}{1.68 \text{ hours}} \]

### Step 4: Calculate the right side of the equation
Calculate \( \frac{42}{1.68} \):
\[ \frac{42}{1.68} = 25 \text{ km/h} \]

### Step 5: Set up the equation
Now we have:
\[ \frac{5}{7} x = 25 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by \( \frac{7}{5} \):
\[ x = 25 \times \frac{7}{5} \]
\[ x = 25 \times 1.4 = 35 \text{ km/h} \]

### Conclusion
The usual speed of the car is \( 35 \) km/h.

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