Trains, Speed, and TunnelsDate: 09/10/98 at 19:16:05 From: Matthew Subject: Trains and Tunnels A freight train is 500m long. It passes through a tunnel 2000m long. Sixty seconds elapse between the time the last car enters and the time the engine exits the tunnel. How fast is the train traveling? I would probably be able to figure this out if I knew the time when the engine enters and exits the tunnel, but I don't know how to calculate the speed the way the question says. I've tried drawing a picture on graph paper, but it doesn't help. I hope you can help me. Thank you. Date: 09/11/98 at 17:00:25 From: Doctor Peterson Subject: Re: Trains and Tunnels Hi, Matthew. It is a little tricky, but when you see it right, it's not too bad. Let's draw a sort of graph, with the distance through the tunnel along the x-axis and time along the y-axis (which I'll draw downward for convenience): tunnel in 2000m out 0+====================+---> <-- at time 0, the last car |\ 500m \ enters the tunnel | \ \ | \ \ | \ train \ | \ \ | \ \ | \ \ 60| \ \ <-- at time 60, the engine V last engine exits the tunnel car You could also just draw a picture of the train and tunnel at the start and end of the 60 seconds, to see where it is: ___________________________ time 0 |500m tunnel | XXXXXX |___________________________| 2000m ___________________________ time 60 | tunnel 500m| XXXXXX |___________________________| At time 0, the engine was 500 m into the tunnel, and at time 60 it was at the end. So in those 60 seconds, the engine traveled (2000 - 500) meters. Now can you finish the problem? - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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