Problem 2-7: The rate at which the North American and European continents are moving apart

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PROBLEM:

The North American and European continents are moving apart at a rate of about 3 cm/y. At this rate how long will it take them to drift 500 km farther apart than they are at present?

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SOLUTION:

We know that the formula for velocity is

velocity=displacementtime\text{velocity}=\frac{\text{displacement}}{\text{time}}

If we rearrange the formula and solve for time, we come up with

time=displacementvelocity\text{time}=\frac{\text{displacement}}{\text{velocity}}

Substituting the given values,

Δt=500 km3 cm/year=5×105 m3 cm/year×100 cm1 m=1.67×107years  (Answer)\begin{align*} \Delta \text{t} & =\frac{500\:\text{km}}{3\:\text{cm/year}} \\ \\ & =\frac{5\times 10^5\text{ m}}{3\:\text{cm/year}}\times \frac{100\:\text{cm}}{1\:\text{m}} \\ \\ & =1.67\times 10^7\text{years} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \\ \end{align*}

Therefore, the time it will take is about 1.67×107 years 1.67\times 10^{7}\ \text{years}.

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