Question

The elevator in the Washington Monument takes 75 seconds to travel 500 feet to the top floor. What is the speed of the elevator in miles per hour? Show your work and explain your reasoning in the space below.

Answer 1

Answer:

The speed of the elevator in miles per hour is $\frac{50}{11}mph$

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,

$1 ft=\frac{1}{5280}mile$

we can multiply both sides by 500

$500\times 1 ft=500\times\frac{1}{5280}mile$

$500ft=\frac{25}{264}mile$

so,

$d=\frac{25}{264}mile$

total time is 75 seconds

now, we can change seconds into hours

we know that

1 hour =3600 seconds

so,

$1 sec=\frac{1}{3600}hour$

we can multiply both sides by 75

$75\times 1 sec=75\times\frac{1}{3600}hour$

$t=\frac{1}{48}hr$

we know that

speed = distance / time

so,

$v=\frac{d}{t}$

now, we can plug values

$v=\frac{\frac{25}{264}}{\frac{1}{48}}mi/h$

now, we can simplify it

$v=\frac{50}{11}mph$

So,

The speed of the elevator in miles per hour is $\frac{50}{11}mph$