SOLUTION: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 575 miles​ apart, their combined travel time is 11 ho

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Question 1192859: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 575 miles​ apart, their combined travel time is 11 hours. If Thaddeus drives at a rate of 50 miles per hour and Ian drives at a rate of 55 miles per​ hour, how long had each been​ driving?
Thaddeus has been driving ____ ​hours, and Ian has been driving ____ hours
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Make this chart

          |  Distance |  Rate  |  Time |
----------------------------------------
Thaddeus  |           |        |       |
----------------------------------------
   Ian    |           |        |       |
----------------------------------------

Fill in their given rates:


          |  Distance |  Rate  |  Time |
----------------------------------------
Thaddeus  |           |   50   |       |
----------------------------------------
   Ian    |           |   55   |       |
----------------------------------------

We want to know their driving times. 
Let x = Thaddeus's time.  Then since their
total driving time is 11, Ian's time is 11-x.
Fill those in:

          |  Distance |  Rate  |  Time |
----------------------------------------
Thaddeus  |           |   50   |   x   |
----------------------------------------
   Ian    |           |   55   | 11-x  |
----------------------------------------

Now since Distance = Rate x Time, we fill in the 
distances by multiplying:

          |  Distance |  Rate  |  Time |
----------------------------------------
Thaddeus  |    50x    |   50   |   x   |
----------------------------------------
   Ian    |  55(11-x) |   55   | 11-x  |
----------------------------------------

Since they are 575 miles apart, and since they
traveled in opposite directions,

Thaddeus' distance + Ian's distance = 575 miles

50x + 55(11-x) = 575

Solve that for x.  That will be Thaddeus's time.
Subtract from 11 and that will be Ian's time.

Edwin
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