Problem 23 - Algebra 2

Question

SPED LIMITS For Exercises 22 and 23 , use the following information. On some interstate highways, the maximum speed a car may drive is 65 miles per hour. A tractor may not drive more than 55 miles per hour. The minimum speed for all vehicles is 45 miles per hour. Write an inequality to represent the speed at which a tractor-trailer may travel on an interstate highway.

Step-by-Step Solution

Answer

The inequality is \( 45 \leq s \leq 55 \).

Step 1: Understanding the Problem

Firstly, let's summarize the given information: a tractor-trailer has a maximum speed limit of 55 miles per hour and a minimum speed limit of 45 miles per hour on some interstate highways.

Step 2: Identifying the Inequality

The speed at which a tractor-trailer may travel can be represented by a variable, say \( s \). We need to write an inequality that captures this range of speeds.

Step 3: Minimum Speed Condition

The tractor-trailer must not go below the minimum speed, which is 45 mph. This can be expressed as: \( s \geq 45 \).

Step 4: Maximum Speed Condition

The tractor-trailer must not exceed the maximum speed, which is 55 mph. This is written as: \( s \leq 55 \).

Step 5: Combining the Conditions

Combine these two conditions to express the complete range of allowable speeds for the tractor-trailer: \( 45 \leq s \leq 55 \).

Key Concepts

Understanding Speed Limits

Speed limits are essential to maintaining safety on roads and highways. They define the legal speed at which different vehicles can travel. On interstate highways, speed limits vary based on vehicle type and specific road regulations. These limits ensure that vehicles move at a harmony-enforced pace, reducing accidents and improving traffic flow.
Speed limits are usually posted clearly on road signs, allowing drivers to adhere to them. The speed limit may differ based on vehicle types; for instance, a car may have a different top speed compared to heavy vehicles like a tractor-trailer. This distinction ensures that larger and potentially more cumbersome vehicles are given appropriate guidelines for safe travel.

What is a Tractor-Trailer?

A tractor-trailer is a heavy-duty vehicle used primarily for transporting goods over long distances. It consists of two main parts: the tractor (the engine unit) and the trailer (cargo-carrying unit). These vehicles are vital for logistics and the transport industry.
Due to their size and weight, tractor-trailers have distinct road regulations, including speed limits, which differ from those of regular cars. They require more distance to stop, have lower acceleration, and this makes adhering to specified speed limits crucial.
Understanding the dynamics of a tractor-trailer helps in appreciating why they have different speed restrictions, aimed at enhancing road safety for all users.

Exploring the Range of Speeds

The range of speeds for a vehicle defines the safe window within which it can operate legally. In this context, the range for a tractor-trailer on interstate highways is defined by the minimum and maximum speed limits. This range ensures that a tractor-trailer can travel efficiently without risking penalties for breaching legal speed bounds.

• Minimum speed is necessary to prevent impeding traffic flow.
• Maximum speed ensures that the vehicle retains manageable control.

A clearly defined range helps to minimize conflicts on the road, allowing for smoother transit and better safety for all vehicles.

Defining Maximum Speed

Maximum speed is the highest velocity at which a vehicle is legally allowed to travel on a specific segment of road. For tractor-trailers on some interstates, the maximum speed is 55 miles per hour.
This limit ensures these large vehicles don't travel too fast, which could increase stopping distances and decrease maneuverability. The purpose is to reduce the potential risks associated with operating these heavy vehicles at high speeds, thereby enhancing road safety.

Minimum Speed Requirements

Minimum speed is the lowest speed a vehicle must travel to avoid being an unnecessary obstacle on the road. For tractor-trailers, this is set at 45 miles per hour on certain interstate highways.
Maintaining a minimum speed helps in avoiding traffic slowdowns and ensures a steady flow of vehicles. For heavy vehicles like tractor-trailers, adhering to the minimum speed ensures they keep up with the general pace of traffic, making it safer for all road users.