Algebra Question: Finding Distance When a Train and Car Meet

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Homework Help Overview

The discussion revolves around a problem in algebra involving relative motion, specifically calculating the distance at which a car catches up to a train. The original poster presents their calculations based on the speeds of both vehicles and the time difference in their departures.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore different methods to set up the equations for distance and time, questioning the original poster's interpretation of the problem and their final answer. Some participants suggest alternative ways to think about the problem, such as considering the distance the train is ahead when the car starts.

Discussion Status

The discussion is active, with participants providing different perspectives on how to approach the problem. Some guidance has been offered regarding the interpretation of the question and the need to solve for distance rather than time. There is no explicit consensus on the correct method yet.

Contextual Notes

Participants note a potential misunderstanding regarding the final goal of the problem, which is to find the distance rather than just the time taken for the car to catch the train. The original poster's calculations are also questioned in terms of their accuracy and relevance to the question posed.

mikefitz
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Train leaves station going 50MPH
Car leaves station going 70MPH - 2 hours later

How far til car catches train?

This should be so simple, here is what I've done:

d=50t
d=70(t-2)

50t=70(t-2)
50t=70t-140
140=20t

I get t=7 miles for my final answer, but according to the book this is wrong. Why?
 
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try it this way: when the car starts the train is 100 miles away. the car makes up ground at 20 miles/hour (70-50)... how many hours does it take to catch the train... how many miles did the car go in that time.
 
How did you get miles from that? If
d=50mph*t hours
d=70mph*(t-2)hours

50mph*t hours=70mph*(t-2)hours
50mph*t hours=70mph*t hours-140 miles
140 miles=20mph*t hours
140miles/20mph = t hours
7 hours = t hours
 
I think the problem is that you've solved for t when the question asks you to solve for d, the distance.

Of course you can now just put t back into one of the equations.
 

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