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Real-Life Activities

Real-Life Math

You're in a submarine using sonar to measure the depth of the ocean floor by transmitting sound waves and measuring them as they're reflected back.

Working with sonar equipment requires a knowledge of math. "High school math at an advanced level is required," says Brad Browne, a sonar technician. "Some basic calculus is involved and math teaches logical thought processes."

Once a sonar technician measures the amount of time it takes for a sound wave to bounce back to the source, the depth of the ocean floor can be calculated.

The formula used to measure distance is:

Distance = Rate x Time, or
D = R x T


This formula is altered a bit to calculate the depth of the ocean. In the new formula:

D = depth
Rate = the speed of sound in water (4,800 feet per second)
Time = the amount of time that it takes for sound to go to and from the sonar source

In this equation:

Time = 1/2 Time (or 0.5T)

The new formula is:

D = R x 1/2 T

If it takes the sonar wave 3.15 seconds to leave the source and come back, what is the depth of the ocean floor that has been measured?