Question

At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other?

Name: Problem 42, Chapter 5: Prealgebra and Introductory Algebra
Uploaded: 2020-07-25T17:47:05-08:00
Duration: 2 min 9 s
Channel: Adnan Gill
Description: At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other?

   At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other?

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 5, Problem 42

Instant Answer

Solved by Expert Adnan Gill

07/25/2020

Step 1

The first train leaves Washington, D.C. one hour before the second train, so it travels for $t+1$ hours. Show more…

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At noon a train leaves Washington, D.C., headed for Charleston, South Carolina, a distance of 500 mi. The train travels at a speed of 60 mph. At 1 P.M. a second train leaves Charleston headed for Washington, D.C., traveling at 50 mph. How long after the train leaves Charleston will the two trains pass each other?

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Key Concepts

Uniform Motion

Uniform motion describes movement at a constant speed in a straight line. This concept implies that the distance traveled can be directly calculated by multiplying the constant speed by the time elapsed, a principle that forms the foundation for solving problems involving objects moving at constant rates.

Relative Speed

Relative speed is the effective speed at which two moving objects approach or separate from each other. In problems where two objects move toward one another, their relative speed is the sum of their individual speeds, which simplifies the process of determining the time until they meet.

Time Offset (Delayed Start)

A time offset occurs when one moving object starts its journey before or after another. This requires adjusting the calculations by considering the head start or delay in the overall time, so that the distance already covered by the object starting earlier is taken into account when determining the meeting point.

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