Quote:
Originally Posted by smhbbag  Quote: |
The train is 3/8 of a bridge from the bridge.
| Where does the problem say this?
It only says:
"A man is 3/8 of the way walking across a railroad trestle when he hears a train approaching at 60 mi/hr."
All we know about the train is its speed, and that the man can hear it when he is on the bridge.
There is no description of where the train is or how far away, relative to the trestle.
If the train is 3/8 of a trestle away from the trestle, then the problem is solvable with a unique solution. But that information wasn't given. |
That information is given in that if he ran the shortest distance to get off the bridge, he would just make it off as the train got to the bridge. The train is as far away from the bridge as it would take to travel in the same time it would take the man to travel 3/8 of the length of the bridge.
Any distances you plug in have to take this into account. Example:
8 mile long bridge. Either direction the man travels, the train will reach the first side of the bridge when he has traveled 3 miles at the speed we're looking for. If he goes away from the train, there will be 2 miles left to go at the moment the train gets to the bridge. The man will have to traverse 2 miles in the same time the train goes 8 miles, which means he will have to move at 1/4 the speed of the train, or 15 MPH.
In this example the train would be 12 miles from the bridge when the man first hears it (pretty good hearing), or 12 minutes away in time. 12 minutes at 15 MPH comes to 3 miles. The train will always be 4 times the distance from the bridge as the man is from the closest side of the bridge, because it is established that the man will cover 1/4 the length of the bridge in the same time it will take the train to travel the entire length of it, and he is therefore traveling at 1/4 the speed.