Let
x--------> the speed of the girl in step
y--------> the speed of the escalator in step
d------> the distance between ground and floor.
we know that
[tex] speed=\frac{distance}{time} \\ \\ time=\frac{distance}{speed} [/tex]
when the girl is going up on escalator
[tex] x-y=\frac{d}{60} [/tex] ----> equation [tex] 1 [/tex]
when the girl is going down on escalator
[tex] x+y=\frac{d}{90} [/tex] -------> equation [tex] 2 [/tex]
Adds equation [tex] 1 [/tex] and equation [tex] 2 [/tex]
[tex] 2x=\frac{d}{60} +\frac{d}{90} \\ \\ 2x=\frac{5}{180} d [/tex]
[tex] x=\frac{5}{360}d [/tex] --------> equation [tex] 3 [/tex]
Time to climb (in step) with y=0 (escalator standing still)
[tex] x*t=d\\\\ t=\frac{d}{x} [/tex] -----> equation [tex] 4 [/tex]
Substitute equation [tex] 3 [/tex] in equation [tex] 4 [/tex]
[tex] t=\frac{d}{\frac{5d}{360}} \\ \\ t=\frac{360}{5} \\ \\ t=72 steps [/tex]
therefore
the answer is
[tex] 72 steps [/tex]
The number of steps she have to take in either direction is [tex]\boxed{72{\text{ steps}}}.[/tex]
Further explanation:
The formula of the speed can be expressed as follows,
[tex]\boxed{{\text{Speed}}=\frac{{{\text{Distance}}}}{{{\text{Time}}}}}[/tex]
The formula of the time can be expressed as follows,
[tex]\boxed{{\text{Time}}=\frac{{{\text{Distance}}}}{{{\text{Speed}}}}}[/tex]
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
[tex]x - y=\dfrac{d}{{60}}[/tex] ......(1)
If a girl is going downward then the speed will be x + y
[tex]x + y=\dfrac{d}{{90}}[/tex] ......(2)
Now add both the equations.
[tex]\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}[/tex]
The time in steps can be calculated as follows,
[tex]\begin{aligned}t&=\dfrac{d}{{\dfrac{{5d}}{{360}}}}\\&=\dfrac{{360}}{5}\\&=72\\\end{aligned}[/tex]
The number of steps she have to take in either direction is [tex]\boxed{72{\text{ steps}}}.[/tex]
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.
