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
. Jill is 48 5/8 inches tall. Lei is 47.5 inches tall. What is the difference in their heights? a. 0.125 inches b. 1.08 inches c
Roman55 [17]

Explanation:

First we write the fraction as a decimal. 5/8 is 0.625, so the height of Jill is 48.625 inches.

The difference is:

48.625-47.5=1.125

Answer:

c. 1.125 inches

5 0
1 year ago
Joanna wants to buy a car. Her parents loan her $5,000 for 5 years at 5% simple interest. How much will Joanna pay in interest?
vova2212 [387]
I= Prt I= 5000*0.05*5 I= $1,250 So she will pay $ 1,250 in interest . I hope that's help !
8 0
3 years ago
All real numbers are whole numbers True or False?
alexandr402 [8]
False. A negative number is real, and doesn't have to be a whole. A fraction is real
5 0
3 years ago
Find the area<br><br> Pls help me<br> Show/explain how to solve ty.
rjkz [21]

Answer:

area = 10 units ^2

Step-by-step explanation:

rectangular area = 2x2 = 4

left side triangle area = 2x2x0.5 = 2

right side triangle area = 4x2x0.5 = 4

4+2+4 = 10

8 0
2 years ago
Ethan ordered 4 sub sandwiches for a party. Each 1/2 sandwich is one serving. Does he have enough to serve 7 friends? How much i
Dima020 [189]
Yes because there is 12
4 0
3 years ago
Other questions:
  • I just put a random answer which is the correct one in this question
    14·1 answer
  • What is 3.3(x-8)-x=1.2
    7·2 answers
  • Find x. (The figure is not drawn to scale.)
    12·1 answer
  • what is the value of y for the line that has a slope of 1 and goes through the points (-4,y) and(-2,8)​
    10·1 answer
  • The suns surface has a grainy texture produced by numerous bright markings called
    7·2 answers
  • Assume running consumes 103 calories per mile. If you run 9-minute mile, what is your average output in watts, during a 1-hour r
    15·1 answer
  • If f(x) = -4x^2 - 6x - 1 and g(x) = -x^2 - 5x + 3, find (f + g)(x).
    7·1 answer
  • (a) A square has a perimeter of 88 m. What is the length of each side?
    15·2 answers
  • Translate to an algebraic statement.<br> "The quotient of twice a number and 7 is 20."
    5·1 answer
  • A window is in the shape of a kite. caleb wants to apply a layer of plastic film on the top half of the window so that the glass
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!