Question 1734: A deer is standing 80m in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 20m from the tunnel. If the deer ran in the opposite direction it would be hit by the train at the Eastern entrance.
How long is the tunnel?
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Sol:
**** 80m ***** L - 80 m
Train <----Deer----------------->
Speed of the deer V, speed of the train 10V.
When the deer running toward the train, the time T it takes is 80/V = T.
and in the same time the train travels 10 V T = 10 V * 80/V = 800 m.
(where it is 20m from the tunnel)
Hence,the diatance from the train to the west entrance of the tunnel is
800+20 = 820 m.
And, we see the dstance between the train and the deer is 820+80 = 900 m.
Assume the lenght of the tunnel is L meters.
When the deer running toward the east, it takes time = 900/(10V - V)=
100/V for the train to reach
(hit) the deer (at the Eastern end).
Hence, L-80 = V (100/V) = 100, and we obtain the length of the tunnel is
180 m.
Kenny
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