Question

You pass a road sign saying "New York \(110 \mathrm{~km}\)." If you drive at a constant speed of \(100 . \mathrm{km} / \mathrm{h}\), how long should it take you to reach New York?

Short answer

It should take approximately 1.1 hours to reach New York at a constant speed of 100 km/h.

Step-by-step solution

Write down the given information

We are given: - Distance remaining to New York: \(110 \mathrm{~km}\) - Constant speed: \(100 \mathrm{~km/h}\)

Apply the formula to calculate time

We will use the formula \(Time = \dfrac{Distance}{Speed}\), so: Time = \(\dfrac{110 \mathrm{~km}}{100 \mathrm{~km/h}}\)

Calculate the time

Now let's do the calculations: Time = \(\dfrac{110}{100}\) = 1.1 hours So, it should take approximately 1.1 hours to reach New York at a constant speed of 100 km/h.

Key concepts

Distance Measurement

Distance measurement is an essential part of many everyday tasks, especially when planning a trip or estimating travel time. In our exercise, the distance from the road sign to New York is given as 110 kilometers. Distances can be measured in various units such as meters, kilometers, miles, etc., but kilometers are commonly used for longer distances, especially in countries using the metric system. When you're given a distance, it's simply a number that tells you how far one point is from another. It helps in figuring out how long it will take to get from start to end when paired with information about the speed at which you'll be traveling. In mathematical problems, distance is often denoted by "D" in equations, like in the formula for calculating time, which we'll discuss later. Remember, accurately measuring distance is key to planning your journey efficiently and ensuring you reach your destination on time.

Speed Calculation

Speed calculation is crucial when we aim to determine how long a journey will take. In our example, the speed is given as a constant 100 kilometers per hour (km/h). Speed tells us how fast an object is moving and is calculated by dividing the total distance traveled by the time taken to travel that distance. The formula can be written as:\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]However, in the given problem, the speed is already provided, and we need it to find the travel time. This means that speed is an indispensable factor for calculating time, especially if we maintain a constant pace throughout the journey. Having a constant speed simplifies calculations and helps us precisely estimate the arrival time at a destination. In real-life situations where speeds can vary, tracking average speed is more challenging but remains essential for accurately planning travel time.

Time Calculation

Time calculation is a fundamental concept when planning trips and is directly linked to distance and speed. In the given problem, we need to find out how long it will take to reach New York. The formula used for time calculation is:\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]Using the formula, if we know the distance (110 km) and the speed (100 km/h), we can easily calculate the time as follows:1. Plug the given values into the formula: - Distance = 110 km - Speed = 100 km/h2. Calculate the time: - \( \text{Time} = \frac{110 \text{ km}}{100 \text{ km/h}} = 1.1 \text{ hours} \) This tells us it will take approximately 1.1 hours to reach New York under the given conditions. Understanding this formula allows anyone to estimate travel time, assuming a constant speed and known distance. This approach is widely used, from daily commuting to professional transportation planning.