Maths Problem needed worked out?

Question

Don't worry, its not for homework or anything.
This morning I had a maths test. And in the maths test was the following question, well something like this.

There was a man walking across a train bridge and he was 2/5 of the way across when he heard a train coming from behind him. He could either run to the other end or run back in the direction he was coming from and he would survive. The train was travelling at 60km/h. How fast did the man have to run to survive?

I found this problem simply impossible. The length of the bridge was not stated and nor how far away the train was!
Could somebody try and work this out and see if it is actually possible before I go and see my maths teacher?

Answer 1

There's not enough information to answer the problem as stated - it depends how far away the train was when he heard it. If (to be a little absurd) he heard it when it was 60 km from the bridge, he'd have at least an hour to get to either end and presumably wouldn't have to go very fast. On the other hand, if the train was almost at the bridge he'd have to run infinitely fast to make it going back.

The only way the problem makes sense is if he only just makes it, with no safety margin in either direction. Then we know that in the time it takes him to run 2/5 of the bridge, the train gets to the near end of the bridge, and in the time it takes him to run 3/5 of the bridge, the train gets to the far end of the bridge. That means the train travels the length of the bridge in the time it takes the man to run 1/5 of the bridge, so he is running at 1/5 the speed of the train or 12 km/h.

Answer 2

I guess that even if you don't know how far away the train is or the length of the bridge, you can still do the calculations and express the answer in terms of these variables. I'm not sure how messy that will be, but I will have a look at it.

Length of bridge = b km
Distance to near end = .4b
Distance to far end = .6b
Speed of train = 60 km/hr
Speed of man = x km/hr

Distance of train from near end = yb km
Distance of train from far end = (y+1)b km

Time for man to reach near end = distance / speed
= .4b / x

Time for train to reach near end = distance / speed
= yb / 60

.4b / x = yb / 60
.4b = ybx / 60
.4 = yx / 60
x = 15/y km/hr where y = number of bridge lengths that the train is from the near end of the bridge.


Time for man to reach near end = distance / speed
= .6b / x

Time for train to reach far end = distance / speed
= (y +1)b / 60

.6b / x = (y +1)b / 60
.6/x = (y +1) / 60
.6 = (y+1)x / 60
x = 36 / (y + 1) where y = number of bridge lengths that the train is from the near end of the bridge.

If the train is one bridge length away from the bridge, the man must run at 15 / 1 = 15 km/hr to reach the near end and 36 / (1 + 1) = 18km/hr to reach the far end.

I'm sure I went about that the long way around, but you can see the idea.