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October 8th, 2008, 12:09 AM   #1
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Need help understanding distance problems

Need help understanding this problem.
A freight train starts from Los Angeles and heads for Chicago at 40 mph. Two hours later a passenger train leaves the same station for Chicago traveling at 60 mph. How long will it be before the passenger train overtakes the freight train?

If I solve this way: (40)t+2 = 60t
t = 4

But, If I solve this way: 40t = (60)t-2
t = 6
For some distance problems it doesn't matter and I get the same answer either way, but for this one, I get different answers.

An example of getting same answer: Sarah leaves Seattle for New York in her car, averaging 80 mph. One hour later a plane leaves Seattle for New York following the same route and flying 400 mph. How long before the plan overtake the car?
(80)t+1 = 400t
t= 1/4

80t = (400)t-1
t = 1/4

My question is why did I get 2 answers, and when solving this type of problem, how do I choose which way of solving is right?
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October 8th, 2008, 04:21 AM   #2
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The first method was correct, but use parentheses correctly: 40(t + 2) = 60t.

The second method doesn't work: 80t = 400(t - 1) doesn't have solution t = 1/4; it gives t = 5/4, which is incorrect.
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