Dimensional Analysis

The Marianas Trench in the pacific ocean is the deepest part of the ocean. The depth is 6.85 mi. The speed of sound under water is 4700 ft/sec. Find the time it takes sound to travel from the surface to the bottom of the Mariannas Trench and back.

6.85 mi x 1 = 6.85/1x 5280 ft/1mi = 35168ft
3168ft x 1ft//4700sec. x60 sec/1min = 46.2 sec

In the second one:

1) How did you get \(\displaystyle \frac{1}{sec}\cdot\frac{sec}{min}\) to end up as seconds?
2) Why did you do that in the first place. You already had seconds. What's the point of changing to minutes?

\(\displaystyle Trench * 2 = 2*6.85*mi\frac{5280*ft}{1 mi}\frac{1 sec}{4700 ft}\)

It's a bit different from yours.

And who "named" this simple problem "Dimensional Analysis"; your teacher? :shock: