Question 574553
Harold Greedy started with $20. After $1 hour, he had $40. It took him 19 more hours to go from $40 to the amount/fortune he wanted. I'll call it X, but I do not have to calculate it.
Horace, started with $40, and increased his fortune at the same rate as his brother had done.
So he got from $40 to X in {{{highlight(19)}}} hours, just like his brother had done before.
My question is, was the official solution to the problem unnecessarily more complicated than that?
JUST FOR FUN (and to apply a little of the stuff you're learning in class)
The brothers' fortunes were increasing in geometric sequence (or geometric progression, depending on book/teacher/country).
After n hours Harold had
${{{20*2^n}}}
After 20 hours he had
X=${{{20*2^20}}}
I still do not have to calculate it
Horace, starting with $40, would have
${{{40*2^t}}} after t hours
When Horace's fortune matched his brother's X=${{{20*2^20}}}, we would have
{{{40*2^t=20*2^20}}} --> {{{2^t=20*2^20/40}}} --> {{{2^t=2^20/2}}} --> {{{2^t=2^(20-1)}}} --> {{{2^t=2^19}}} --> {{{log(2, 2^t)=log(2, 2^19)}}} --> {{{highlight(t=19)}}}
OK. I'm curious. I'll calculate it after all.
X=${{{20*1048576}}}=$20,971,520