While completing these, Q1 refers to the question in which we are given a 'number of minutes going at 60mph'. Q2 refers to the question in which we move at 60mph for a certain distance.
At first, I didn't have any major problems. However, when I completed the Q2, I noticed that the generalization for Q1 and Q2 had the same coefficients! Given that the variables we were plugging in are different (a 'time' for Q1 and a 'distance' for Q2) something felt wrong. See below for my investigation of this.
Q1:
Q2:
After converting the Q2 generalization to 'minutes', we see identical coefficients. This was confusing and warranted further investigation:
Looking through my work, I realized that the '10' in Q1 is assumed to have units 'mph'. This balances with the units on the bottom of the fraction, meaning that the 'time' units for t2 will be the same as t1.
In Q2, because we are multiplying t1 by our initial speed (60mph), the final value for time is ALSO in hours. This yields my original equation for t2. However, when I convert this to minutes, I see that we still get the same coefficients. This was confusing!
Finally, I realized that because our initial speed is 60mph, 25 min = 25 miles. This means that when we are travelling at 60mph, the magnitude of minutes that passes is equal to the magnitude of miles we travel. We are travelling at 1mile/min. This explains why we have identical coefficients in both equations. When we re-write the Q2 formula to be any unit of time other than minutes, the coefficients will be different.
Interesting twist!
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