Chapter 4: Problem 17

The Pacific Plate moves north relative to the North American Plate at a rate of \(6 \mathrm{~cm}\) per year. How long will it take Los Angeles (a city on the Pacific Plate) to move northward by \(480 \mathrm{~km},\) the present distance between Los Angeles and San Francisco?

Short Answer

Expert verified

It will take \(8,000,000\) years for Los Angeles to move northward by \(480 \: km\), the present distance between Los Angeles and San Francisco.

Step by step solution

Convert distance to the same unit

We need to convert the desired distance to the same unit as the given rate, which is centimeters. There are 100,000 centimeters in 1 kilometer, so we can convert 480 kilometers to centimeters by multiplying by 100,000. \( 480 \: km * 100,000 \: cm/km = 48,000,000 \: cm \) The desired distance is 48,000,000 cm.

Calculate the time it takes to cover the distance

Now that we have the desired distance in the same unit as the rate, we can calculate how long it will take to cover the distance by dividing the desired distance by the rate: \( time = \frac{distance}{rate} \) \( time = \frac{48,000,000 \: cm}{6 \: cm/year} \)

Simplify the result

Let's simplify the fraction to find the time in years: \( time = 8,000,000 \: years \) It will take 8,000,000 years for Los Angeles to move northward by 480 km, the present distance between Los Angeles and San Francisco.

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The Pacific Plate moves north relative to the North American Plate at a rate of \(6 \mathrm{~cm}\) per year. How long will it take Los Angeles (a city on the Pacific Plate) to move northward by \(480 \mathrm{~km},\) the present distance between Los Angeles and San Francisco?

Short Answer

Step by step solution

Convert distance to the same unit

Calculate the time it takes to cover the distance

Simplify the result

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