John Speed

The elevators in the John Hancock building in Chicago move 521ft in 23s. What is their speed in meters per sec?

Answer in units of mi/h.

This is a simple problem if you know how to convert from one thing to another. But first let’s find out haw fast this thing is going in feet per second: v = 521ft / 23s = 22.65ft/s.

Now all we have to do is the converting. Let’s review what we will need to know. We need to know that there are 3 feet in a yard. We have to know that there are 1.09 yards in a meter. We have to know that there are 5280 feet in a mile. Finally, we have to know that there are 3600 seconds in one hour.

Here we go! Wait! Before we get started you probably should get a blank sheet of paper and write down what I put here except that you should write the fractions vertically. I would do that myself if I could but the format here is limited. Write the fractions vertically so that you can see more easily what is going on.

22.65ft / s x (1yd / 3ft) x (1m / 1.09yd) = 22.6 x 1 x 1m / s x 3 x 1.09 = 22.6m / 3.27 = 6.91m/s.

To get to miles per hour:
22.65ft / s x (1mi / 5280ft) x (3600s / 1h) = 22.6 x 1mi x 3600 / 5280 x 1h = 81360mi / 5280h = 15.4 mi/h

So, get to know your conversion factors! They can be really helpful. By the way, here’s another one you might find handy: To convert from m/s to mi/r you need to know that there are 1609m in one mile. So: m/s x (1mi / 1609m) x (3600s / 1h) = 3600 / 1609 = 2.24. So, multiply the number of meters per second by 2.24 and you will have the speed in miles per hour. If you divide the miles per hour number by 2.24 you will have the speed in meters per second. Cool!

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