+113 Mary and John have 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 and took 18 seconds to reach the top. How many steps does the escalator have in total?
+118687 Mary and John have both completed a trip up an escalator.
The speed and number of steps on the escalator is set.
So the time the escalator takes is also set - assuming no steps
Let there be x steps in 1 trip.
John took 15 steps on the way up and took 12 seconds to reach the top.
\(\frac{x-15}{12}\) steps per sec
Mary took only 7 steps and took 18 seconds to reach the top. How many steps does the escalator have in total?
\(\frac{x-7}{18}\) steps per sec
These are equal
\(\frac{x-15}{12}=\frac{x-7}{18}\\ 18(x-5)=12(x-7)\\ 3(x-5)=2(x-7)\\ 3x-45=2x-14\\ x=31 steps\)
The escalator has 31 steps.
+118687 Mary and John have both completed a trip up an escalator.
The speed and number of steps on the escalator is set.
So the time the escalator takes is also set - assuming no steps
Let there be x steps in 1 trip.
John took 15 steps on the way up and took 12 seconds to reach the top.
\(\frac{x-15}{12}\) steps per sec
Mary took only 7 steps and took 18 seconds to reach the top. How many steps does the escalator have in total?
\(\frac{x-7}{18}\) steps per sec
These are equal
\(\frac{x-15}{12}=\frac{x-7}{18}\\ 18(x-5)=12(x-7)\\ 3(x-5)=2(x-7)\\ 3x-45=2x-14\\ x=31 steps\)
The escalator has 31 steps.
the reasoning for the answer by this melody person is incorect
the real resoning should be,
once you get to solving for x,
Step 1: Cross-multiply.
x-15/12=x-7/18
(x−15)*(18)=(x−7)*(12)
18x−270=12x−84
Step 2: Subtract 12x from both sides.
18x−270−12x=12x−84−12x
6x−270=−84
Step 3: Add 270 to both sides.
6x−270+270=−84+270
6x=186
Step 4: Divide both sides by 6.
6x=186
x=31
