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Answer: The elevator takes 20 seconds to travel from first floor to sixteenth floor.
Step-by-step explanation: Given that an elevator takes 4 seconds to travel from the first floor to fourth floor.
We are to find the time taken by the elevator to travel from first floor to the sixteenth floor.
Number of floors between first floor and fourth floor = 4 - 1 = 3,
and
number of floors between first floor and sixteenth floor = 16 - 1 = 15.
So, time taken by the elevator to travel 3 floors = 4 seconds.
Time taken by the elevator to travel 1 floor [tex]=\dfrac{4}{3}~\textup{seconds}.[/tex]
Therefore, time taken by the elevator to travel 15 floors will be
[tex]\dfrac{4}{3}\times15=4\times5=20~\textup{seconds}.[/tex]
Thus, the elevator takes 20 seconds to travel from first floor to sixteenth floor.
Elevator takes [tex]\boxed{20{\text{ seconds}}}\\[/tex] to reach sixteenth floor from first floor.
Further explanation:
Given:
It takes an elevator 4 seconds to travel from the first floor to the fourth floor.
Explanation:
The total floors travelled by the elevator in 4 seconds can be calculated as follows,
[tex]\begin{aligned}{\text{Total floors}} &= 4 - 1 \\ &= 3 \\\end{aligned}[/tex]
Consider the time taken by the elevator to reach sixteenth floor from first floor as [tex]y{\text{ seconds}}.[/tex]
Total floors between first and sixteenth can be calculated as follows,
[tex]\begin{aligned}{\text{Total floors}} &= 16 - 1\\&= 15\\\end{aligned}[/tex]
The time taken by the elevator to reach sixteenth floor from first floor can be obtained as follows,
[tex]\begin{aligned}\frac{4}{y} &= \frac{3}{{15}}\\4 \times 15 &= 3 \times y\\60 &= 3y\\\frac{{60}}{3} &= y\\20 &= y\\\end{aligned}[/tex]
Elevator takes [tex]\boxed{20{\text{ seconds}}}[/tex] to reach sixteenth floor from first floor.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: elevator, 4 seconds, first floor, fourth floor, sixteenth floor, travel, long, takes, numbers, slope, slope intercept, equation,
