We can convert this problem into a simple algebra problem.
if we make the second train equal to X, then the first train will be X+22
And since the trains are coming towards each other, we can and these numbers together, to get 2x+22
So, the MPH of the trains is 2x+22.
Since the trains meet in 5 hours, we can divide 1130 by 5 and get 226, and we know that 2x+22=226.
From here, it is easy 2x is equal to 204, and x is equal to 102,
so the rate of the first train is 102+22, and the second train is 102, so the rate of the two trains is 124, and 102.
Okay I will try to explain this as best as I can.
If the members were not allowed to hold two positions, the answer would be 25*24*23.
This is because there are 25 people who can run for the first spot, and 24 people who can run for the second, because
the first spot would be taken, and there will only be 24 people availible for the second. Same goes with the 23. (I hope I am not making this confusing.)
But because we can't do that, we have to try something else. If a member can hold two spots, the number of spots will be
25*25*24. This accomendates for two spots and allows a member to have two positions. 25*25*24 is equal to 15,000
So there are 15,000 combinations.
This problem is pretty simple if we think about it in a different way.
We see the we have 1 - 2 + 3 - 4 +... + 2005 - 2006 + 2007 - 2008 + 2009 - 2010.
It looks hard, but all we have to see are the -1.
1-2 is equal to -1, 3-4 is equal to -1, and so on.
Now, all we have to do is figure out how many -1 s we have.
the biggest number is 2010, and if we divide that by 2, (because every two numbers is a -1) we get 1005.
From this, we can conclude that the answer is -1*1005=-1005