1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lutik1710 [3]
3 years ago
8

a girl wants to count the steps of a moving escalator which is going up. if she is going up on it, she counts 60 steps. if she i

s walking down, taking the same time per step, then she counts 90 steps. how many steps would she have to take in either direction, if the escalator were standing still?
Mathematics
2 answers:
Leto [7]3 years ago
5 0

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

speed=\frac{distance}{time} \\ \\ time=\frac{distance}{speed}

when the girl is going up on escalator

x-y=\frac{d}{60} ----> equation 1

when the girl is going down on escalator

x+y=\frac{d}{90} -------> equation 2

Adds equation 1 and equation 2

2x=\frac{d}{60} +\frac{d}{90} \\ \\ 2x=\frac{5}{180} d

x=\frac{5}{360}d --------> equation 3

Time to climb (in step) with y=0 (escalator standing still)

x*t=d\\\\ t=\frac{d}{x} -----> equation 4

Substitute equation 3 in equation 4

t=\frac{d}{\frac{5d}{360}}  \\ \\ t=\frac{360}{5} \\ \\ t=72 steps

therefore

the answer is

72 steps

kramer3 years ago
4 0

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 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.

You might be interested in
Solve kx + 7 = 4 for x.
Leya [2.2K]

Answer:

4

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Justine runs 250 yards in 50 seconds.
DaniilM [7]

Answer:

a: 300 Yards

b: 10 seconds

c: 5 Yards per second

7 0
3 years ago
A box contains several slips of paper. There is one slip for every even number between 13 and 21. Without looking, you draw one
PolarNik [594]
The answer is d you're welcome
5 0
3 years ago
WILL GIVE A BRAINLIEST
skelet666 [1.2K]
Find slope
slope betwen 2 points (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)

so
first make denoms same
denom is 10
(4/5,1/5) turns to (8/10,2/10)
(1/2,3/2) turns to (5/10,15/10)
slope=(15/10-2/10)/(5/10-8/10)=(13/10)/(-3/10)=13/-3=-13/3

use point slope
use (4/5,1/5)
y-y1=m(x-x1)
a point is (x1,y1) and slope is m
y-1/5=-13/3(x-4/5)
expand
wait, we don't need to do that, the only one with slope -13/3 is D
answer is D
4 0
3 years ago
In which situation do the quantities combine to make 0? A Kurt deposited $50 into his checking account on Friday. The next week,
poizon [28]
C. The temp at 10pm was 6°C. Over the next 3 hours, the temp dropped 2°C/hr.

6 -2(3) = 0
8 0
3 years ago
Other questions:
  • Which statement describes a unit cube?
    9·1 answer
  • Tameron is driving 540 miles to college. If he drives at an average rate of 45 miles per hour, how many hours will it take him t
    8·1 answer
  • the Circle fit in a square with a side of 12 inches what is the approximate area of the shaded region between the square in the
    7·2 answers
  • (2x^3 z^2)^3 / x^3 y^4 z^2 * x^-4 z^3
    10·1 answer
  • The distance, d, measured in miles, that Hye drove is d = 45.2t, where t is the time in hours.
    10·2 answers
  • Tyler took 33 photos while on a class field trip. This is 3 times as many photos as Kayla took. Which equation can be used to fi
    6·1 answer
  • Please help! i’ve been stuck on this for over 10 minutes.
    11·1 answer
  • What function? If correct ill give u the rest of 200 points please help
    9·2 answers
  • PLEASE HELP!! THIS IS MY LAST QUESTION PLEASE!!<br> (Answeer all the problems)
    9·2 answers
  • Find the surface area of the prism.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!