Chapter 27, Problem 3TS

To determine

The time to form one large city by the Los Angeles and San Francisco due to movement of plates.

Answer to Problem 3TS

The time for the formation of one large city by Los Angeles and San Francisco is $1.714\times {10}^7\text{yr}$.

Explanation of Solution

Given info: The present distance between the Los Angeles and San Francisco is $600\text{km}$ and the rate of slide of one plate to another plate is $3.5\text{cm}/\text{yr}$.

Write the expression for time for the formation of one large city.

$n=\frac{d}{r}$

Here,

$n$ is the time for the formation of one large city

$d$ is the present distance between the Los Angeles and San Francisco

$r$ rate of movement of one plate to another

Substitute $600\text{km}$ for $d$ and $3.5\text{cm}/\text{yr}$ for $r$ in the above expression to get $n$.

$\begin{array}{c}n=\frac{600\text{km}}{\left(3.5\text{cm}/\text{yr}\times \frac{1\text{km}/\text{yr}}{{10}^5\text{cm}/\text{yr}}\right)}\\ =1.7143\times {10}^{\mathrm{}}\text{yr}\end{array}$

Conclusion:

Therefore, the time for the formation of one large city by Los Angeles and San Francisco is $1.7143\times {10}^7\text{yr}$.