Expert: Scott A Wilson - 3/10/2010

Question
one train leaves a station heading west. 2 hours later a second train leaves the same station heading east. the second train is traveling 15 mi/h faster than the first. six hours after the second train leaves,the two trains are 580 miles apart. find the rate at which each trains is traveling.  thanks sir! :)

Answer
Since it is 6 hours after the second train left, and it left 2 hours after the first train,
the first one has distance 8s.  The second train has speed s+15 and has been going for 6 hours,
so the distance is 6(s+15).

Thus, the 580 miles is given by the sum of the two distances, or 8s + 6(s+15) = 580.

Multiply out the 6(s+15) to get 6s + 90, right?

Add on to 8s, and you should get 14s + 90.

Subtract 90 from both sides and the equation become 14s = 490.

Now all we have left to do is say that s = 490/14.
Now I recognized that 5x14=70 and 7x70=490, so s = 5*7.

Now we both know what 5*7 is, right?  That's the answer.

That is the speed s of the first train.  To get the second train speed, note that it is s+15.