Escaping the Tunnel
Two boys walking in the woods decided to take a shortcut through a railroad tunnel. when they had walked two-third of the way through the tunnel, their worst fears were realized. A train was coming from the opposite direction, nearing the tunnel entrance. The boys panicked and each ran for a different end of the tunnel. Both boys ran at the same speed, 10 miles per hour. Each boy escaped the tunnel just at the instant that the train would have squashed them into the rails.
Assuming the trains' speed was constant, and both boys were capable of instantaneous reaction and acceleration, how fast was the train going ?
Assuming the trains' speed was constant, and both boys were capable of instantaneous reaction and acceleration, how fast was the train going ?
Labels: friday special, puzzle
posted by Rajesh Lal at
9:57 PM
9 Comments:
30 miles per hour
I agree. 30 miles an hour.
ejrm_1978
I agree because to get there at the same time, the train would have to travel 3x faster to travel more distance in the same time
but that would be to get to the end of the tunnel at the same time, which in the question, it states the train didnt.
so that would mean its anything less than 30mp/h
Ok then, let me try to explain this to you.
Lets sya that the tunnel is 3 miles long. If they have already walk 2/3 of the way that would mean that they have walk 2 of the 3 miles of that tunnel before they saw the train. One of the boys ran toward the train while the other ran away from the train. Running at 10 mph would be 6 minute to run 1 mile and 12 minutes to run 2. By the time boy A (the one who ran toward the train)reached the end of the tunnel, the train reached the entrance. Boy B has be running at the same time. He has already ran 1 mile and has one more to go. It will take him 6 minutes to get to the end of the tunnel. At 30 mph the train will take 6 minutes to travel 3 miles at 2 minutes a mile. So by the time it takes boy B to travel the 6 minutes to run that last miles the train will just have missed boy A, travel 3 miles, than miss boy B.
I hope that helps.
ejrm_1978
is it 26.66666666 ? dont round that up incase you get the poor lad's ankles squashed by a train
The train was going 15mph. The time that the train took to get to the other side was equal to the time it took for one boy to run 2/3 back to the tunnel. Distance equals rate times time. Time equals distance divided by rate. If D equals 1/3 of the tunnel then the one boy ran 2 times D and the train went 3 times D. Therefore 2D divided by 10mph equals 3 times D divided by the rate of the train. So the D's cancel and 2 is to 10 as 3 is to FIFTEEN.
David C
David, your forgetting that the other boy ran 1/3 of the tunnel to the other entrance (where the train was coming in) before the train even got to the tunnel. In that time the other boy will have ran 1/3 of the tunnel back and be only 1/3 away from the exit when the train enters. So the answer is 30 mph.
um... 79mph?
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