We can measure the rate of erosion in this canyon at about...

We can measure the rate of erosion in this canyon at about $0.01$ inches/year. Based on this rate, when did the canyon start to erode? (Hint: Measure the difference in elevation from the bottom of the canyon at the latitude and longitude given above and the top, measured at the road on the edge of the canyon due south of the previous point. Then divide by the rate of erosion. Make sure to use the correct units.) a. 750,000 years b. $1,200,000$ years c. $2,700,000$ years d. $3,500,000$ years

We can measure the rate of erosion in this canyon at about $0.01$ inches/year. Based on this rate, when did the canyon start to erode? (Hint: Measure the difference in elevation from the bottom of the canyon at the latitude and longitude given above and the top, measured at the road on the edge of the canyon due south of the previous point. Then divide by the rate of erosion. Make sure to use the correct units.)
a. 750,000 years
b. $1,200,000$ years
c. $2,700,000$ years
d. $3,500,000$ years

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Key Concepts

Rate of Erosion

This concept involves determining how quickly a material (such as rock in a canyon) is worn away over time. It requires understanding that erosion is a gradual process measured in terms of a change per unit time, and it is fundamental in geological studies that compute the age of geological formations by dividing the total change by the rate of change.

Unit Conversion

Unit conversion is essential in problems involving measurements to ensure that all quantities are expressed in compatible units before performing calculations. This concept ensures that when comparing or dividing rates and measurements, consistency is maintained, thus avoiding errors in the final calculation.

Time Calculation from Rate and Change

This concept involves calculating the time required for a process to occur by dividing the total change (e.g., total erosion amount or difference in elevation) by the rate at which that change happens. It is a common method in physics and geology to estimate the duration over which gradual processes have taken place.

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