Learn Before
Finding Express and Local Train Speeds Using Equal Distances
Apply the distance, rate, and time problem-solving strategy to find two unknown speeds when both travelers cover the same distance but at different rates and times.
Problem: An express train and a local train leave Pittsburgh to travel to Washington, D.C. The express train makes the trip in hours and the local train takes hours. The express train's speed is miles per hour faster than the local train's speed. Find the speed of both trains.
- Read and draw: Sketch both trains traveling from Pittsburgh to Washington, D.C., and note the equal distances. Create a rate–time–distance table:
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Express | |||
| Local |
- Identify: The speed of each train.
- Name: Let = the speed of the local train, so the express train's speed is . Multiply rate by time to fill in the distance column.
- Translate: Because both trains travel the same route, their distances are equal:
- Solve: Distribute on the left: . Subtract from both sides: . So the local train travels at mph. The express train's speed is mph.
- Check: Express: miles. Local: miles. Both distances are miles.
- Answer: The local train's speed is mph and the express train's speed is mph.
This example demonstrates the equal-distance scenario: when two travelers cover the same route, their distance expressions are set equal to each other. Using a single variable for the slower speed and expressing the faster speed as keeps the equation in one unknown, and the distributive property is used to solve it.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.3 Math Models - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Finding Distance Given Rate and Time
Finding Time Given Distance and Rate
Uniform Motion Problems
Finding Express and Local Train Speeds Using Equal Distances
Matching Units in the Distance, Rate, and Time Formula
Elapsed Time in Distance, Rate, and Time Problems
In the context of transportation and logistics, which variable in the formula d = rt represents the constant speed of a vehicle?
Match each variable from the distance formula (d = rt) to its corresponding meaning in a transportation and logistics context.
In a professional logistics environment, when calculating the total distance a vehicle travels at a constant speed, the formula d = rt is used. In this relationship, the variable 'r' represents the ____.
In a professional logistics context, the standard distance formula () is applicable for calculating the total distance traveled specifically when a vehicle moves at a uniform (constant) rate of speed.
Fundamental Formula for Distance in Transportation
Standardizing Route Calculations at Swift Logistics
A logistics coordinator needs to calculate the total travel time for a delivery truck. Arrange the following steps in the correct algebraic order to derive the formula for time () from the standard distance formula ().
Standard Distance Calculations for Fleet Operations
In a transportation performance report, a logistics coordinator needs to calculate the constant rate of speed () maintained by a vehicle. If the total distance () and the time elapsed () are known, which of the following correctly expresses the formula for rate?
In a logistics route planning system, if you are provided with the total distance () of a shipment route and the constant rate of speed () of the delivery vehicle, which algebraic formula must you recall to calculate the estimated travel time ()?
Rate and Speed Terminology in Uniform Motion
Learn After
A logistics manager is comparing an express delivery service and a local delivery service that both travel the same route between two cities. When setting up an equation to find their speeds, which of the following is the correct relationship to use?
A logistics coordinator is comparing a freight train and a passenger train that both travel the same route between two major shipping hubs. To set up an equation to find their unknown speeds, the coordinator must identify that the ____ traveled by both trains is identical.
A logistics coordinator is using the 'Equal Distance' strategy to find the speeds of two delivery vehicles that traveled the same route between two distribution centers. Arrange the following steps in the correct order to set up the problem-solving equation.
A transportation coordinator is using the 'Equal Distance' strategy to compare the speeds of an express delivery truck and a local delivery truck traveling the same route. Match each algebraic component or principle with its correct role in setting up the problem-solving equation.
True or False: In a logistics model where an express delivery truck travels 15 miles per hour faster than a local delivery truck, and the local truck's speed is represented by 'r', the correct algebraic expression for the express truck's speed is r + 15.
Solving Equal Distance Equations in Logistics
Core Principles of Equal Distance Logistics Modeling
Verifying Delivery Data at Swift-Link Logistics
A logistics analyst has just calculated the speeds of two delivery trucks that traveled the same route between two shipping hubs. To verify that their solution is correct using the 'Equal Distance' strategy, which verification step should the analyst recall?
A logistics coordinator is using the 'Equal Distance' strategy to find the speeds of two delivery trucks. After setting up the equation 4(r + 12) = 5r to represent the identical distances traveled, which algebraic property must the coordinator use to multiply the 4 by both the 'r' and the '12'?