SOLUTION: Mary and John both completed a trip up an escalator. John took 15 steps on the way up and took 12 seconds to reach the top. Mary took only 7 steps up, and took 18 seconds to reach

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Question 927340: Mary and John both completed a trip up an escalator. John took 15 steps on the way up and took 12 seconds to reach the top. Mary took only 7 steps up, and took 18 seconds to reach the top. how many steps does the escalator have in total?
A) 28
B) 29
C) 30
D) 31
E) 32
Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the escalator be u%28stairs%2Fsecond%29.
John took 15steps on the way up and took 12 seconds to reach the top.

Mary took only 7 steps up, and took 18 seconds.

Since the length of the escalator is constant:

15stairs+%2B12second%2Au+=+7stairs+%2B+18second%2Au =>

15stairs+-+7stairs=18%2Au-12second%2Au

8stairs=6second%2Au+

8stairs%2F6second=u+

u=+%284%2F3%29%28+stairs%2F+second%29

Therefore, the total length of the escalator:

15stairs+%2B12%2Au

=

=15stairs+%2B4%2A4stairs

=15stairs+%2B16stairs
=31stairs

answer is: D) 31