Train Travel. A train leaves Union Station for Central Station, 216 km away, at 9 A.M. One hour

Name: Problem 76, Chapter 3: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-31T18:29:01-08:00
Duration: 2 min 25 s
Channel: Ankit Gupta
Description: Train Travel. A train leaves Union Station for Central Station, 216 km away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M. and the first train at 10: 30 A.M. they would still have met at noon. Find the speed of each train.

step 1 In this question, we have to find the speed of the trains. Let's consider the first situation wh

Question

Train Travel. A train leaves Union Station for Central Station, $216 \mathrm{km}$ away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at $9 \mathrm{A.M.}$ and the first train at $10: 30 \mathrm{A.M.}$ they would still have met at noon. Find the speed of each train.

   Train Travel. A train leaves Union Station for Central Station, $216 \mathrm{km}$ away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at $9 \mathrm{A.M.}$ and the first train at $10: 30 \mathrm{A.M.}$ they would still have met at noon. Find the speed of each train.

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 3, Problem 76

Instant Answer

Solved by Expert Ankit Gupta

07/31/2020

Step 1

Let's denote the distance from Union Station to the meeting point as $x$ km. Show more…

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Train Travel. A train leaves Union Station for Central Station, $216 \mathrm{km}$ away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at $9 \mathrm{A.M.}$ and the first train at $10: 30 \mathrm{A.M.}$ they would still have met at noon. Find the speed of each train.

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Key Concepts

Systems of Equations in Motion Problems

By establishing equations that represent the distances each object travels over time and equating their sum to the known total distance, one can set up a system of linear equations. Solving this system allows for finding the unknown speeds or times associated with the motion.

Uniform Motion (Distance-Time Relationship)

This concept states that when an object moves at a constant speed, the distance it covers is the product of its speed and the time traveled. It is fundamental to solving problems where the time, speed, and distance are linearly related.

Relative Motion in Opposing Directions

When two objects move towards each other from different starting points, their effective or relative speed becomes the sum of their individual speeds. This principle is crucial for determining when and where the objects will meet.

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