Geologists estimate that a certain continent moves at a constant rate

Question

Geologists estimate that a certain continent moves at a constant rate of 1 inch every 3 years.

Assume:
• 1 mile = 63,360 inches
• 1 year = 365 days

Approximately how many days will it take the continent to move a distance of 0.001 mile?

A. 6.3 × 10^3
B. 2.0 × 10^4
C. 6.9 × 10^4
D. 1.9 × 10^5
E. 6.9 × 10^5

Dereno · Answer

The continent moves at a constant rate of 1 inch every 3 years.

1 mile = 63,360 inches.

So, for 0.001 mile takes how many days.

If, 1 mile = 63,360 inches.

then 0.001 mile = 63,360 * 0.001 = 63.36 inches.

Then, if moving 1 inch takes 3 years = 3*365 days

1 inch = 3*365 days

63.36 inches = ?

= 3 * 365 * 63.36

= 69,379.2

=  approx 6.9 * 10^4

Option C

chetan2u · Answer

Of course, solution is straight forward wherein we have to convert miles to inches and years to days. The most important thing here would be how fast we get to our answer.

0.001 mile would mean 63360/1000 or 63.36

1 inch in 3 years or 3*365 days
So, 63.36 inches in 3*365*63.36
Now let us approximate as answer choices are far off.
3*365*63.36 ~ 3*400*60 =  72000 = 7.2*10^4 
 6.9*10^4 is the closest with no other choices anywhere close to the approximate value.

C

Edskore · Answer

Good solves above — I want to add the full reasoning because this type of question catches a lot of people out under time pressure.

Key concept tested: Multi-Step Unit Conversion with Scientific Notation

The common trap: students try to convert miles → years directly and get tangled in the chain. The cleaner approach is to convert miles to inches first, then inches to years, then years to days — one conversion at a time.

Step 1 — Convert the target distance to inches
0.001 miles × 63,360 inches/mile = 63.36 inches

Step 2 — Convert inches to years
The rate is 1 inch every 3 years, so:
63.36 inches × 3 years/inch = 190.08 years

Step 3 — Convert years to days
190.08 years × 365 days/year = 69,379 days

Step 4 — Express in scientific notation
69,379 ≈ 6.9 × 10^4 → Answer: C

The trap most people fall into: they see "approximately" and round too early — for example, rounding 63,360 to 60,000 before multiplying, which nudges the answer toward 6.3 × 10^4 (Option A). Always carry the full conversion through and approximate only at the final step when expressing in scientific notation.

A second trap: forgetting to convert miles to inches entirely and working directly with 0.001 miles × 3 years × 365 days, which gives a completely off answer.

Takeaway: On unit conversion PS questions, write out the full chain — distance → rate unit → time unit — before you calculate anything, so no conversion step gets skipped under exam pressure.

Geologists estimate that a certain continent moves at a constant rate

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Geologists estimate that a certain continent moves at a constant rate

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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