SOLUTION: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 355 miles​ apart, their combined travel time

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Question 1061259: Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 355 miles​ apart, their combined travel time is 11 hours. If Thaddeus drives at a rate of 30 miles per hour and Ian drives at a rate of 35 miles per​ hour, how long had each been​ driving?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Accounting for time quantities seems like a good way to think this, but not so good trying to see points on a time line. All we know of time is the sum of their travel times.
PERSON           SPEED           TIME        DISTANCE
Thaddeus          30              t
Ian               35              i
Total                             11           355


PERSON           SPEED           TIME        DISTANCE
Thaddeus          30              t            30t
Ian               35              i            35i
Total                             11           355



-
Distance sum,

-
Solve this system for the times, t and i:
.
Use the Elimination Method.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Thaddeus and Ian start at the same location and drive in opposite​ directions, but leave at different times. When they are 355 miles​ apart, their combined travel time is 11 hours. If Thaddeus drives at a rate of 30 miles per hour and Ian drives at a rate of 35 miles per​ hour, how long had each been​ driving?
Let time Thaddeus spent driving be T

Then time Ian spent driving = 11 – T

We then get the following DISTANCE equation: 30T + 35(11 – T) = 355

30T + 385 – 35T = 355

30T – 35T = 355 – 385 

– 5T = - 30

T, or time Thaddeus spent driving = 

Time Ian spent driving: 

It is that simple.....NOTHING COMPLEX!! 

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