Speed of Two TrainsDate: 7/31/96 at 13:50:14 From: Anonymous Subject: Two Trains Word Problem This problem from my math book has haunted me for weeks... A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m. One hour later, a train leaves Indianapolis for Chicago. They meet at noon. If the second train had started at 9 a.m and the first train at 10:30 a.m., they would still have met at noon. Find the speed of each train... I know that the answer is: First train 36km/hr, second train 54 km/hr But how? I made the following charts: Original Trip: If Changes To Schedules Made: Distance Rate Time Distance Rate Time Train 1 d1 r1 3 Train 1 d1 r1 1.5 Train 2 216-d1 r2 2 Train 2 216-d1 r2 3 I have plugged the answers in every which way but I can't find the proper sequence of equations that when substituted make the answers match... Any help in this would be greatly appreciated. Thanks! Date: 7/31/96 at 14:21:48 From: Doctor Robert Subject: Re: Two Trains Word Problem You have made a very good start. The only thing that you haven't realized is that once you fill out 2 of the boxes in a line, the third one follows from relationship distance = rate * time. In the original trip distance(1) = 3*r1 and distance(2) = 2*r2, so that 3r1+2r2 = 216 The "changes" box gives us 1.5(r2) + 3r2 = 216 This system solves to give the answers you quote. I hope that this helps. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/31/96 at 15:53:39 From: Josephine Montiel Subject: Re: Two Trains Word Problem I would like to thank Dr. Robert for the fast response. I still need clarification on one point. At the point where you say: "In the original trip distance (1) = 3*r1 and distance (2) = 2*r2, so that 3r1+2r2 = 216 The "changes" box gives us 1.5(r2) + 3r2 = 216, This system solves to give the answers you quote. " How did you get to the point 1.5(r2)? From my chart I can only see 1.5(r1). I know these are related, but I can't pull it out myself, so can you detail this part for me? j.m. Date: 8/1/96 at 22:58:50 From: Doctor Robert Subject: Re: Two Trains Word Problem My boo-boo. You are right. The two equations are, I think, if I don't make another boo-boo: 3r1 + 2r2 = 216 1.5r1 + 3r2 = 216 Sorry. Bad typing fingers. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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