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? Give your answer to two significant digits.
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I order to solve this problem we use: `distance = rate* time.`
In algebraic terms it is `d = rt,`
where `d = 500,`
`t = 75.`
So this gives us `500=75r.` Divide both sides by 75.
`500/75 = (75r)/75` `rArr` `6.67 = r`
Which means the rate is 6.67 feet/second. Now convert to miles per hour.
There are 5280 feet in 1 mile, and 3600 seconds in 1 hour.
Therefore we get: `(6.67 ft) / (1 sec) * (1mi) / (5280 ft) * (3600 sec) / (1 hour)`
Which yields: `5.45mph`
To determine this, we would divide the distance by the time:
speed = distance/time
But, we need miles per hour. We are given feet and seconds. So, we need to convert. There are a couple of ways to convert. The easiest to explain is probably with proportions, as in:
We know that there are 5280 feet in 1 mile, so we can make a ratio of 5280 feet/1 mile. Then, with the 500 feet, we can make a proportion as:
5280 feet = 500 feet
1 mile x
And, we solve for x. We need to make sure that feet are "paired" together as such. So, x = 500/5280 = 25/264 miles
Then, we do the same for the time. 60 seconds in a minute, 60 minutes in an hour. So, 3600 seconds in an hour. So, we can make 1 hour/3600 seconds. And:
1 hour = x (seconds have to be paired together)
3600 sec 75 sec
So, here, x = 75/3600 = 1/48 hour
So, speed = distance/time = (25/264)/(1/48) = 4.55 miles per hour.
Good luck, Asian girl. I hope this helps.
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