Question 1073420
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a) Solve using on variable. Two trains depart simultaneously from a station, traveling in opposite directions. 
One average 80 km/h and the other 100 km/h. Determine how long it will take the trains to be 450 km apart.

b) Solve using two variables. Two trains depart simultaneously from a station, traveling in opposite directions. 
One average 8 km/h more than the other, and after 1/2 hour they are 100 km apart. Determine the speed of each train.
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<pre>
a) Let t be the time under the question.
   Then  the distance traveled by the first  train is  80*t kilometers,
   while the distance traveled by the second train is 100*t kilometers.

   The equation is 

       80t + 100t = 450,  or

       180t = 450,  which gives  t = {{{450/180}}} = {{{5/2}}} = 2.5 hours = 2 hours and 30 minutes.


<U>Answer</U>.  2.5 hours = 2 hours and 30 minutes.


b) Let x be the speed of the first train and y be the speed of the second train.

   Then you have these equations:

       x    -    y =   8,   (1)

       0.5x + 0.5y = 100.    (2)

    From (2), express x = y + 8, and substitute it into (2). You will get

      0.5(y+8) + 0.5y = 100,   or

      0.5y + 4 + 0.5y = 100,

      y = 100 - 4  --->  y = 96.

<U>Answer</U>.  The speed of the second train is 96 km/h;  of the first train 96 + 8 = 104 km/h.
</pre>

Solved.