Problem 50 - Algebra 1: Concepts and Skills

Question

The elevator in the Washington Monument in Washington, D.C., climbs at a rate of about 400 feet per minute. What is the elevator's speed?

Step-by-Step Solution

Answer

The speed of the elevator is 400 feet per minute.

Step 1: Understand the problem

The elevator climbs at a rate of 400 feet per minute. This means in one minute, the elevator covers a distance of 400 feet. The speed of the elevator is thus given directly by the problem.

Step 2: Apply the definition of speed

The speed of an object is defined as the distance it travels divided by the time it takes to travel that distance. In this case, the distance is 400 feet and the time is 1 minute. Hence, the speed of the elevator = \(\frac{distance}{time} = \frac{400 feet}{1 minute} = 400 feet/minute\).

Key Concepts

Distance Rate Problem

Distance rate problems revolve around the basic relationship between distance, rate, and time. Understanding this relationship is crucial for solving various practical scenarios, such as the one involving the elevator in the Washington Monument.

• Distance is how far an object travels.
• Rate refers to the speed at which the object travels.
• Time is the duration the object takes to travel that distance.

These problems often ask you to calculate one of these quantities when the other two are known. The key formula that ties these elements together is: \[ \text{Distance} = \text{Rate} \times \text{Time} \]Knowing how to manipulate this formula allows you to solve questions like, "How far does an elevator travel in a certain time at a given speed?" These problems require a good understanding of multiplication, division, and unit conversions.
Sometimes you may need to adjust units to ensure they are compatible, like converting hours to minutes or miles to feet. All these skills help in tackling various distance rate problems effectively.

Distance and Time

The concepts of distance and time are fundamental in understanding how objects move. Distance is simply the length between two points, while time is the measurable period during which an event occurs. In our elevator problem, distance represents how far the elevator travels vertically up the monument, and time is how long it takes to make this movement.

• To find the distance covered, you'd multiply the rate by the time: \[ \text{Distance} = \text{Rate} \times \text{Time} \]
• If you need to find the time taken, rearrange the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]

These calculations help understand the relationship between how long something takes and how far it goes.
When solving these types of problems, it's essential to maintain consistency in units. This might mean keeping all time units in minutes or hours and distance in feet or meters, depending on what's given. Understanding these fundamentals makes solving complex movement-related problems much simpler.

Rate of Travel

Rate of travel describes how fast something is moving. It's an important concept in physics and everyday scenarios alike. For example, the elevator’s speed of 400 feet per minute is its rate of travel.

• The rate is typically expressed as distance per unit of time, like miles per hour or feet per minute.
• To determine the rate, use this relation: \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \]

Understanding rate helps in planning and calculating travel times and distances.
If you're given the distance and need to find the time, or vice versa, the rate of travel provides a handy link between these two quantities.
In practice, knowing the rate of travel allows you to predict how long it will take to reach a destination or how far you will go in a given time. It simplifies various tasks, from engineering to road trips, making it a valuable skill to master.