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