Train and TunnelDate: 07/18/2001 at 08:04:05 From: Matthew Subject: Word Problems A freight train 800 metres long is travelling at a constant speed of 18km per hour. The front of the train enters a tunnel 1.6km long at exactly 1:00 p.m. At what time does the rear of the last carriage of the train emerge from the tunnel? Date: 07/19/2001 at 13:00:59 From: Doctor Ian Subject: Re: Word Problems Hi Matthew, The first thing I do with a problem like this is draw a picture, so I can keep track of what I know and what I need to find out. 1600m ()))))))))))))))) 1:00 [][][][] 800m 1:00 + t1 [][][][] 1:00 + t2 [][][][] Now, this suggests an easy way to solve the problem. We can think of the train as moving its own length three times: ()))))))))))))))) [][][][] [][][][] [][][][] [][][][] So the last car will emerge from the tunnel at 1:00 + 3T, where T is the amount of time that it takes for the train to travel its own length. The train moves 18,000m in 60 minutes. So how long does it take the train to move 800m? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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