SOLUTION: An athlete runs up a set of stadium stairs at a rate of 2 stairs a second, turns around and descends those same stairs at a rate of 3 stairs per second. If the workout takes 90 sec

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Question 1018280: An athlete runs up a set of stadium stairs at a rate of 2 stairs a second, turns around and descends those same stairs at a rate of 3 stairs per second. If the workout takes 90 seconds, how long does it take him to run UP the stairs.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
RT=D travel rates rule
Time is seconds, distance in steps
             rate      time(seconds)      distance(how many steps)
UP           2          d/2                  d
DOWN         3          d/3                  d
TOTAL                    90



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

An athlete runs up a set of stadium stairs at a rate of 2 stairs a second, turns around and descends those same stairs at a rate of 3 stairs per second. If the workout takes 90 seconds, how long does it take him to run UP the stairs.
Let time taken to run up the stairs be T

Then time it takes him to run down = 90 - T

The distance equation is thus formed: 

2T = 270 - 3T

2T + 3T = 270

5T = 270

T, or time taken to run up the stairs = , or  

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