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Find the time it takes sound to travel from the surface, to the bottom of the Marianas Trench and back.

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

Hi Ryan;
Your first priority is to consider the fact that one unit is in miles, whereas the other is in feet/second.
We must convert.  The conversion factor is...
1 mile/5,280 feet
(4700 ft/sec)(1 mile/5280 ft)
We must cancel units...
(4700 feet/sec)(1 mile/5280 feet)
0.89 miles/sec
We need to isolate the factor of time.
time=[(2)(6.85 miles)]/(0.89 miles/sec)
time=[(2)(6.85 miles)]/(0.89 miles/sec)
Because 1/0.89/sec=sec/0.89--something that is doubly divided is its inverse multiplied.
time=(13.7)(1 sec/0.89)
time=15.39 sec
Let's check our work...
(2)(6.85 miles) ?  (0.89 miles/sec)(15.39 sec)
Let's cancel units...
(2)(6.85 miles) ? (0.89 miles/sec)(15.39 sec)
Let's multiply...
13.70 ? 13.70
This is a question about unit conversions. One thing you will notice is that there are two different units distance measurements. One is in feet and one is miles. First, we need to convert the feet to miles or vice versa to get going.
Converting 4700 feet to miles involves a really weird decimal (4700/5280 = 0.890151515...). Since such decimals are awkward to use, let's convert the 6.85 miles into feet.
6.85 miles * 5280 feet/mile = 36168 feet. This whole number is much nicer to work with!
Now that both distance measurements are in feet, let's find out how long it takes for the sound to go down to the bottom. We must invert the feet per second ratio to get feet on the bottom of the fraction and cancel out to find seconds.
1 second / 4700 feet * 36168 feet = 36168 / 4700 = 7.69 seconds.
Since it is a two-way trip, double the time:
7.69 seconds * 2 = 15.39 seconds.