Wendy took a trip from davenport to omaha a distance of 300mi. she traveled part of the way by bus which arrived at the train station just in time for wendy to complete her journey by train. the bus averaged 40 mph and the train averaged 60 mph the entire trip took 5.5 hours. how long did wendy spend on the train?

Wendy spent four hours on the train.
If the...
Train Speed= 60 mph
Train Time= x
Bus Speed= 40 mph
Bus Time= 5.5-x
Total Time= 5.5 hr
and 
Total Distance= 300 miles
Then we can put all of that into the equation...
60x + 40(5.5-x)= 300
Now, following the order of operations we can free the x from the parenthesis by multiplying 40 by 5.5 and (-x) to get...
60x + (-40x) + 220= 300
Next we can simplify by adding the 60x and (-40x) to get...
20x + 220= 300
After that we need to get the x alone on the left side.  To do this we must use reverse order;  if we subtract 220 from 220 on the left side and then we can subtract 220 from 300 on the left side.  Remember the Golden Rule of Algebra! If you add, subtract, multiply, divide, or raise to a power on one side you must do it on the other!  This gives us...
20x + 220 - 220= 300 - 220
20x= 80
Now all that is left to get x all alone on the left is to look back at the golden rule of algebra and divide 20 from both 20x and 80.  Which gives us...
20x/20 = 80/20
x= 4

And that gives us our answer!  4 hours :D

Hope this helped!