The number of steps she have to take in either direction is \(\boxed{72{\text{ steps}}}.\)
Further explanation:
The formula of the speed can be expressed as follows,
\(\boxed{{\text{Speed}}=\frac{{{\text{Distance}}}}{{{\text{Time}}}}}\)
The formula of the time can be expressed as follows,
\(\boxed{{\text{Time}}=\frac{{{\text{Distance}}}}{{{\text{Speed}}}}}\)
Given:
If a girl is going up then the numbers of steps she counts are 60.
If a girl is going down then the numbers of steps she counts are 90.
Explanation:
Consider the speed of the girls be “x”.
Consider the speed of the escalator be “y”.
Consider the distance between the ground and the floor will be “d”.
If a girl is going upward then the speed will be x - y
\(x - y=\dfrac{d}{{60}}\) ......(1)
If a girl is going downward then the speed will be x + y
\(x + y=\dfrac{d}{{90}}\) ......(2)
Now add both the equations.
\(\begin{aligned}x - y + x + y&=\frac{d}{{60}}+\frac{d}{{90}}\\2x &=\frac{{90d+60d}}{{60 \times 90}}\\2x&=\frac{{150d}}{{5400}}\\2x&= \frac{{5d}}{{180}}\\x&=\frac{{5d}}{{360}}\\\end{aligned}\)
The time in steps can be calculated as follows,
\(\begin{aligned}t&=\dfrac{d}{{\dfrac{{5d}}{{360}}}}\\&=\dfrac{{360}}{5}\\&=72\\\end{aligned}\)
The number of steps she have to take in either direction is \(\boxed{72{\text{ steps}}}.\)
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Number system
Keywords: Girl, count, steps, moving escalator, going up, 60 steps, same time, direction, standing still, walking down.
