How Do You Solve a Train Speed Problem with a Snow-Drift Interruption?

[mathemagician]

Hi everyone, I am new to these forums and thought this would be a good place to get some help.

I picked up a three dollar russian made math problem book at a local book sale. I am working on the questions it has in it and I came across the first problem on motion it has and I can't quite figure it out. This is high-school level stuff by the way so I would hope its easy for many here.

Problem:

The train left station A for station B. Having traveled 450 km, which constitues 75 percent of the distance between A and B, the train was stopped by a snow-drift. Half an hour later the track was cleared and the engine-driver, having increased the speed by 15 km per hour arrived at station B on time. Find the initial speed of the train.

I have tried to visualize the problem. This is what I have come up with.

http://www3.sympatico.ca/markroxas/motionproblem1.GIF"

The question has no total time and you have to find speed. So are there two unknowns to solve? And how do I do that in this problem? Or is there a different way to solve this? Thanks for any help.

 

[himanshu121]

Let the required time be T

If there would have been no problem due to snow then the train wud have reached the station B in time T

Now find sepearate times for two part of motion arising dua to a break of 0.5 hr + the time for break equate it will T

 

[himanshu121]

Mathematical Form

$$\frac{D}{v}=\frac{3D}{4v}+\frac{D}{4(v+15)}+ 0.5$$

 

[uart]

Note that this problem does require an assumption that is not explicitly stated in the problem discription (but which could however be quite reasonably argued as being "common sense"). The assumption of course is that the inital speed of the train was precisely the correct speed to make the train arrive at the destination exactly on time.