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.

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

distance=(rate)(time)

We need to isolate the factor of time.

time=(distance)/(rate)

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...

distance=(rate)(time)

(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

13.70=13.70