Problem Solving

If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)

In one day you get 24 * 60 = 24 * 12 * 5 = 288 * 5 minutes. That means that 2 880 000 = 288 * 10 000 = 288 * 5 * 2000 is 2000 days before the said time. Since 717 = 600 + 117 = 11h and 57 minutes, you get that the time was 6p.m. 27 mins - 11 h 57 mins = 6 a.m. 30 mins.

Hey Dana, can you explain your thought process or reasoning that made you choose factoring to solve this problem? I think your solution is probably the quickest way to get to the answer, and I understand the solution, but what I don't know is how do you see this problem and figure out that you can solve it using factoring? do you just use trial and error and continue once you notice that 288*5 makes 1 day? Or do you just assume that factoring should be used since your dealing with such a large number?

Well, let me try to explain... Hope you understand smth of this...
What immediately caught my eye was that 2 880 000 in the number that you provided. I was like: oh man, what do I do with this tiny thing over here? It's obvious you're supposed to turn it into days, but dividing 2 880 000 by 24h * 60 mins seemed a bit too much. So I started doing what I always do: factorization.

Now here comes the fun part: since numbers are my faves, I learned most of the important powers of numbers in 7th and 8th grade and they've stuck to my brain like glue up until now. For instance, try to learn all the squares of numbers up to 15 ( = 225). I also learned quite a few cubes (3^3 = 27, 6 ^3 = 216 and so on) and some other useful powers of numbers (243 = 3^5, 1024 = 2^10 etc...). So I noticed quite quickly that 288 = 2 * 144 = 2 * 12^2 = 2*12*12 = 24 * 12.
Another number thing that stuck to my head is that 60 = 12 * 5 (or, for that matter, that 48 = 16 * 3, to give you another example of "sticky" multiplications). Since I was looking for 24 * 60, the obvious thing was that 24 * 60 = 24 * 12 * 5 = 288 * 5.

Now, I know I might have disappointed you a bit... Because this is no standard way of solving the problem... It's just experience ( = romanian math teachers force feeding you math until college) and working a lot with numbers... So if you are really looking for smth more solid and general, my explanation is very, very crappy....

hahaha... I guess seeing the answer options changes everything! But probably solving more factoring problems will help in recognizing number patterns like you explained. Thanks!