The vampire Martin is traveling on a train that is 0.5 miles long and moving at a steady clip of 50 miles per hour. The train enters a two-mile-long tunnel at exactly 2:00 PM. How much time does Martin have to drink from his next victim before the rear of the train emerges from the tunnel?

Here's the question again for those who work in metric. The vampire Martin is traveling on a train that is 0.5 kilometres long and moving at a steady clip of 50 kilometres per hour. The train enters a two-kilometre-long tunnel at exactly 2:00 PM. How much time does Martin have to drink from his next victim before the rear of the train emerges from the tunnel?



* Solutions will be given in terms of miles. For those who prefer to work in metric terms, simply substitute kilometres for miles. The distances are not equivalent, of course, but Martin has three minutes to drink from his victim before the rear of the train emerges from the tunnel.

How long a vehicle takes to travel a particular distance is determined by the distance and the speed at which the vehicle is moving. The train on which Martin is riding must travel 2.5 miles* for the engine to completely pass through the 2 mile tunnel and for the 0.5 mile train body to emerge. The train is known to be traveling at a speed of 50 mph. Since the distance(D) a vehicle travels is found by multiplying its speed(S) by the amount of time(T) it travels, or D = S x T, the answer to how much time it will take Martin's train to pass completely through the tunnel can be found by substituting the known values into the equation and solving for time. Thus:

D = S x T
2.5 mi = 50 mph x T
2.5mi/50mph = T
.05 hr = T

What is .05 (or 5%) of an hour? An hour is 60 minutes, so 5% of an hour is 60 x .05 = 3 minutes.

If time/speed/distance problems are not your forte, there are other ways this problem could have been solved without the use of the TSD equation. Here are some solutions that I've seen used and which require deductive reasoning more than remembering the TSD equation:

1. If it takes 60min/50min = 1.2 minutes for the train to travel 1 mile, it must take 1.2 min/hr x 2.5 mi = 3 minutes for the train to travel the entire distance of 2.5 miles.

2. If the train travels 50/60 = .83 miles per minute, it will take 2.5 mi/.83 mpm = 3 minutes to travel the entire distance of 2.5 miles.

3. If the train can make 50 mph/2.5 mi = 20 increments of 2.5 miles in 1 hour, each of those increments will take 60 min/20 = 3 minutes.

4. If the train takes 2 mi/50 min = .04 hrs to go 2 miles, it takes .02 hrs to travel 1 mile, and .01 hrs to travel 1/2 mile. Therefore, to travel 2.5 miles, it will take .04 hrs + .01 hrs = .05 hrs x 60 min = 3 minutes to travel the entire distance.

5. The train is traveling at 50 mph and going 2.5 miles, so 50 mph is to 60 minutes as 2.5 miles is to how many minutes?

50 mph 2.5 mi
------ : ------ , so 50X = 60(2.5) which, solving for X =
60 min X
X = [60(2.5)]/50
X = 150/50
X = 3 minutes

6. The train can make the following distances in the following amounts of time:

50 miles in 1 hour
25 miles in 1/2 hour
12.5 miles in 15 minutes
2.5 miles in 3 minutes

By whatever method you choose to solve the problem, Martin will have 3 minutes to drink from his victim before the rear of the train completely emerges from the tunnel. The question now to be asked is how much blood can a blood-drinker drink if the blood- drinker could drink blood in 3 minutes?