Answer:
The speed of the elevator in miles per hour is [tex]\frac{50}{11}mph[/tex]
Step-by-step explanation:
We are given
The elevator in the Washington Monument takes 75 seconds to travel 500 feet to the top floor
so,
total distance is 500 ft
Firstly, we will change feet to miles
we know that
1 mile = 5280 feet
so,
[tex]1 ft=\frac{1}{5280}mile[/tex]
we can multiply both sides by 500
[tex]500\times 1 ft=500\times\frac{1}{5280}mile[/tex]
[tex]500ft=\frac{25}{264}mile[/tex]
so,
[tex]d=\frac{25}{264}mile[/tex]
total time is 75 seconds
now, we can change seconds into hours
we know that
1 hour =3600 seconds
so,
[tex]1 sec=\frac{1}{3600}hour[/tex]
we can multiply both sides by 75
[tex]75\times 1 sec=75\times\frac{1}{3600}hour[/tex]
[tex]t=\frac{1}{48}hr[/tex]
we know that
speed = distance / time
so,
[tex]v=\frac{d}{t}[/tex]
now, we can plug values
[tex]v=\frac{\frac{25}{264}}{\frac{1}{48}}mi/h[/tex]
now, we can simplify it
[tex]v=\frac{50}{11}mph[/tex]
So,
The speed of the elevator in miles per hour is [tex]\frac{50}{11}mph[/tex]
