Question

Some geologists are finding evidence that suggests that this one-mile deep canyon may have been cut within the last 4 million years. Assuming a uniform rate of erosion and without considering canyon widening due to slope retreat, calculate how much (in millimeters per year) the Colorado River would have to downcut per year to form this mile-deep canyon in 4 million years. Show your work and clearly indicate what each quantity represents.

Answer 1

The number that Colorado River would have to downcut per year to form the mile-deep canyon in 4 million years is 0.40 millimeter per year.

Depth of canyon = 1 mile

Time taken = 4 million years

Based on the above information, the rate will be:

= Depth / Time taken

= 1 mile / 4 million years

= 0.25 mile / million year

Note that 1 mile = 1609344 millimeter

Therefore, the rate will be:

= (0.25 × 1609344) / 1000000 years

= 0.40 millimeter / years

In conclusion, the rate is 0.40 millimeter per year.

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