Story problems for Algebra II/Trig review test

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SUMMARY

The discussion centers on a problem involving two trains departing from points B and C, with B heading East at 90 mi/h and C heading West at 100 mi/h. The trains start 450 miles apart, with the train from B leaving at noon and the train from C leaving 15 minutes later. To determine when the trains will meet, one must formulate an expression for the distance between them over time, setting it to zero to find the intersection point.

PREREQUISITES
  • Understanding of linear equations and distance-time relationships
  • Basic knowledge of algebraic expressions
  • Familiarity with graphing concepts
  • Ability to solve equations for a variable
NEXT STEPS
  • Learn how to set up and solve distance-rate-time problems
  • Study the concept of relative speed in motion problems
  • Explore graphing techniques for linear equations
  • Practice solving word problems involving two moving objects
USEFUL FOR

Students studying Algebra II or Trigonometry, educators teaching motion problems, and anyone looking to improve their problem-solving skills in algebraic contexts.

roquel
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Homework Statement


at noon a train leaves B heading East at 90 mi/h to C which is 450 miles away
at 12:15 pm a train leaves C heading West to B at 100 mi/h. When will they pass each other?


Homework Equations

t=0 when train leaves B and train leaving C is ) at t=15min



The Attempt at a Solution

Graph hours on the x-axis and miles on the y axis, but how do you graph the train leaving C? I don't see how the lines intersect. Where do I go to get basic information on these types of problems?
 
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You don't need to graph anything.

Let t be the number of hours since noon that have elapsed.
Can you write down an expression in terms of t for how far apart the trains are?
(hint: they start 450 miles apart and one train leaves earlier)

Once you have done that, they will pass each other at a time t that makes your expression equal zero (because then they will be zero miles apart!)
 

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