Understanding the Problem

The question asks us to find the length of a bridge. We are given the speed at which a car crosses the bridge and the time it takes to cross it. This is a typical distance, speed, and time problem.

Given Information

• Speed of the car: 54 km/hr
• Time taken to cross the bridge: 1.7 minutes

Formula Required

The relationship between distance, speed, and time is fundamental. The formula is:

$Distance = Speed × Time$

To find the length of the bridge, we will use this formula. The length of the bridge is the distance the car covers while crossing it.

Calculations

1. Unit Conversion

The speed is given in kilometers per hour (km/hr), but the time is given in minutes. To use the formula correctly, we need consistent units. Let's convert the time from minutes to hours.

There are 60 minutes in 1 hour.

So, 1.7 minutes can be converted to hours as follows:

$ \text{Time in hours} = \frac{1.7 \text{ minutes}}{60 \text{ minutes/hour}} = \frac{1.7}{60} \text{ hr} $

2. Calculating the Distance (Bridge Length)

Now we can use the formula $Distance = Speed × Time$ with the converted time.

$ \text{Length of Bridge} = \text{Speed} \times \text{Time in hours} $

$ \text{Length of Bridge} = 54 \frac{\text{km}}{\text{hr}} \times \frac{1.7}{60} \text{ hr} $

First, let's simplify the calculation:

$ \text{Length of Bridge} = \frac{54 \times 1.7}{60} \text{ km} $

Multiply the speed by the time:

$ 54 \times 1.7 = 91.8 $

Now, divide this result by 60:

$ \text{Length of Bridge} = \frac{91.8}{60} \text{ km} $

$ \text{Length of Bridge} = 1.53 \text{ km} $

Conclusion

The calculation shows that the length of the bridge is 1.53 km. This matches one of the options provided.