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

Options

A. ` 17 ( 6)/(7) `km/hr
B. ` 25 km//hr`
C. ` 30 km//hr`
D. ` 35 km//hr`

Answer

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

### Step 1: Convert the time from hours, minutes, and seconds to seconds.
The time given is 1 hour, 40 minutes, and 48 seconds.

1 hour = 3600 seconds (since 1 hour = 60 minutes and 1 minute = 60 seconds)
40 minutes = 2400 seconds (40 minutes * 60 seconds)
48 seconds = 48 seconds

Now, we add these together:
\[ \text{Total time in seconds} = 3600 + 2400 + 48 = 6048 \text{ seconds} \]

### Step 2: Set up the equation for speed.
The speed of the car is given as \( \frac{5}{7} \) of its usual speed (let's denote the usual speed as \( x \)).

The formula for speed is:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

The distance covered by the car is 42 km, which is equal to 42000 meters (since 1 km = 1000 meters).

Thus, we can write:
\[ \frac{5}{7} x = \frac{42000 \text{ meters}}{6048 \text{ seconds}} \]

### Step 3: Solve for \( x \).
To find \( x \), we can rearrange the equation:
\[ x = \frac{42000 \times 7}{6048 \times 5} \]

Now, let's calculate the right-hand side:
1. Calculate \( 42000 \times 7 = 294000 \).
2. Calculate \( 6048 \times 5 = 30240 \).

Now substitute these values back into the equation:
\[ x = \frac{294000}{30240} \]

### Step 4: Simplify the fraction.
Now, we simplify \( \frac{294000}{30240} \):
\[ x = 9.7 \text{ (approximately)} \]

### Step 5: Convert the speed from meters per second to kilometers per hour.
To convert from meters per second to kilometers per hour, we multiply by \( \frac{18}{5} \):
\[ \text{Usual speed in km/h} = 9.7 \times \frac{18}{5} \]

Calculating this gives:
\[ \text{Usual speed in km/h} = 9.7 \times 3.6 = 35 \text{ km/h} \]

### Conclusion:
The usual speed of the car is **35 km/h**.

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