How Many Trains Meet?Date: 09/17/2001 at 19:16:07 From: Eric Subject: Trains leaving every hour on the hour Every hour, on the hour, a train leaves Tallahassee for Jacksonville, while another train leaves Jacksonville for Tallahassee. The trip between the two cities takes exactly two hours. How many trains going in the opposite direction will a Tallahassee train to Jacksonville meet? Please help. Date: 09/18/2001 at 10:46:32 From: Doctor Ian Subject: Re: Trains leaving every hour on the hour Hi Eric, I find it hard to think about something like this without a picture, so let's try drawing one. At any given hour, we have one train ready to leave both cities: []\ Tallahassee ========================================= Jacksonville ========================================= /[] We also have a train arriving at both cities (i.e., the ones that departed two hours ago): []\ []\ Tallahassee ========================================= Jacksonville ========================================= /[] /[] Finally, we have a train halfway between, going in each direction (i.e., the ones that departed an hour ago): [1]\ [2]\ [3]\ Tallahassee ========================================= Jacksonville ========================================= /[4] /[5] /[6] So this is the situation at any time t=0. Now, let's pick a train leaving from Tallahassee (#1), and see what happens to it. It's not clear from the description of the problem whether train 1 'passes' train 4 as it pulls out of the station, so I'll leave that for you to work out with your teacher. But a few minutes after the hour, we have this situation: [1]\ [2]\ Tallahassee ========================================= Jacksonville ========================================= /[5] /[6] After one hour, we have this situation: [7]\ [1]\ [2]\ Tallahassee ========================================= Jacksonville ========================================= /[5] /[6] /[8] Train 1 has passed train 5, and is just about to pass train 6. Another hour later, we have this situation: [9]\ [7]\ [1]\ Tallahassee ========================================= Jacksonville ========================================= /[6] /[8] /[9] So train 1 has passed train 8, and again, it remains to be negotiated whether train 1 also passes train 9. Can you take it from here? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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