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# Escalator

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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?

jonathanxu999  Nov 25, 2017

#1
+91962
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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.

Melody  Nov 26, 2017
Sort:

#1
+91962
+2

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.

Melody  Nov 26, 2017
#2
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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

Guest Dec 2, 2017

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