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I just graduated from college studying math and this problem really seems like there are too many variables to be solved.
Basically, if x is sunrise, a is speed of car leaving city A and b is speed of car leaving city B:
16 - x = 500 / a (500 miles at a miles per hour = 16 (hours after midnight) - x (time car left)
21 - x = 500 / b
Two equations, three unknowns. Even adding in the bit about them passing each other at noon, we get two new variables, call them i and j which are the distances from A and B respectively when they pass at noon, so:
12 - x = i / a
12 - x = j / b
Now we have 4 equations 5 unknowns. Still seems unsolvable.
I believe that it is a difficult one for 12 years old. May be those are questions that separate the top performers?
For bravity, here is the solution
Let t be the sunrise
Let Va and Vb be the speed by driver A and B, respectivily
Let x1 and x2 be the distance trvaled by A and B, resppectively when they meet at noon (12).
One equation comes from the total distance travel by both which is the same
(16 - t)Va = (21- t)Vb since both traveled 500 (in fact that 500 number is never used and dosesn't matter in Mile or Km)
Now at noon, each traveled the same time ( t = distance/speed), therefore
x1/Va = x2/Vb, then again each of them completed the remaining distance taking 4 and 9 hours respectively. Incorporating that gives
9Vb/Va = 4Va/Vb
This gives Va/Vb = 3/2 or 1.5
Inserting this on the first equestion gives
t = 6.
Therefore, sunrise was at 6 am.
Congratulations! You have the right answer, and your reasoning is flawless. Sunrise was at 6 am. And the distance between the cities (500 miles) was a "red herring." The distance could have been 500 feet or 5,000,000 miles; the answer would have been the same, sunrise at 6 am.
I'm surprised that some were angry with me for posting the problem. There is not a "mathematical puzzle" forum on this board. But I was (pleasantly) surprised that I had the number of responses that I did.
I'll post one more puzzle on this board in a few days (a Chinese puzzle for eighth grade students) that is a little more more difficult. If you see my name under the title "Chinese puzzle" you can safely ignore it. Then I'll disappear for a few weeks.
Well they obviously must not be driving cars that were made in Russia
This alludes to a valid point. If this thread is intended to be testament to how technologically advanced a country is based on education requirements.... Russia could not be any worse of an example.
Compared to the rest of the developed world, they suck. Not to mention their detestable practice of engineering ethics... something that is only surpassed by the chinese.
Sweet, someone figured it out! Was a totally different path than i was going down. I'd agree that we need to improve the schools here in the U.S., same time that's probably an argument for one of the political boards.
I believe that it is a difficult one for 12 years old. May be those are questions that separate the top performers?
For bravity, here is the solution
Let t be the sunrise
Let Va and Vb be the speed by driver A and B, respectivily
Let x1 and x2 be the distance trvaled by A and B, resppectively when they meet at noon (12).
One equation comes from the total distance travel by both which is the same
(16 - t)Va = (21- t)Vb since both traveled 500 (in fact that 500 number is never used and dosesn't matter in Mile or Km)
Now at noon, each traveled the same time ( t = distance/speed), therefore
x1/Va = x2/Vb, then again each of them completed the remaining distance taking 4 and 9 hours respectively. Incorporating that gives
9Vb/Va = 4Va/Vb
This gives Va/Vb = 3/2 or 1.5
Inserting this on the first equestion gives
t = 6.
Therefore, sunrise was at 6 am.
Ok, I see where I went wrong. I had my equations set up similarly but for some reason I had 9pm as 22 hrs, and there is something else slightly different about my procedure.
I struggle to see the usefulness of such a problem. I think that reflects the real shame.
I use stuff like this on occasion to solve problems at work.
This particular type of problem is more often just a tool to teach logical thought and application of substitution.
It's like a "widget" example in a finance class, guns and butter in an economics course or sitting there drawing pictures of fruit in an art class.
Basics to teach a concept.
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Was a totally different path than i was going down. I'd agree that we need to improve the schools here in the U.S., same time that's probably an argument for one of the political boards.
