How to Set Up Algebraic Expressions for Car Travel Problems?

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SUMMARY

This discussion focuses on setting up algebraic expressions for a car travel problem involving two cars: Car A, traveling at a constant speed of 50 mph, and Car B, traveling at a variable speed V greater than 50 mph. The problem requires the formulation of equations to determine the distance and time relationships between the two cars as they travel and rest. Key questions include how far Car B is ahead of Car A when it stops, the position of Car A when Car B resumes travel, and the timing of their encounters at specific markers.

PREREQUISITES
  • Understanding of algebraic expressions and equations
  • Knowledge of speed, distance, and time relationships
  • Familiarity with the formula V = D/T
  • Basic problem-solving skills in physics or mathematics
NEXT STEPS
  • Research how to derive equations from speed, distance, and time relationships
  • Learn about setting up piecewise functions for variable speeds
  • Explore examples of similar car travel problems in algebra
  • Study the implications of rest periods on travel time calculations
USEFUL FOR

Students studying algebra, educators teaching problem-solving techniques, and anyone interested in applying mathematical concepts to real-world travel scenarios.

fatuma205
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Homework Statement



Two cars start at the same time from the same place and travel along the same road. Car A has a constant speed of 50mph. Car B travels with the constant speed V for 100 miles, then stops to rest for a time, T, then travels again with constant speed V for another 100 miles. Assume V is greater than 50mph.

Homework Equations



I was trying to set up the equations but have trouble with it but here is what I have so far.
Car A= 50mph
Car B= Vmph + 100miles

The Attempt at a Solution



I got stuck at trying to come up with algebraic expressions.
 
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It is not clear to me what you are solving for. Do both cars travel the same distance?
 


The first thing they asked was to write an algebraic expressions as answers to the follwing questions.
1. How far is B ahead of A when B stops to rest?
2. Where is A when B starts up again
3. What time is it when A passes a marker 150 miles from the starting point?
4. suppose we were at the 150 mile marker. how long would we have to wait between the passing of A and the passing of B?
5. Where is A when B arrives at a point 200 miles from its starting point.

I need to step up an algebraic expression in order to answer these questions and from the information they gave me don't know how to step up the formula. In class we used so far V=D/T
thank you
 

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