Puzzles with numbers and things

[davis_greatest]

OK. Sunrise occurs at 6a.m.

Suppose
- sunrise occurs s hours before noon
- Person 1 travelling to A travels at speed a (units of distance per hour)
- Person 2 travelling to B travels at speed b (units of distance per hour)

Then distance between A and B can be expressed in 3 different ways:

(1) a(s+4) [total distance travelled by Person 1]
(2) b(s+9) [total distance travelled by Person 2]
(3) as + bs [sum of distances travelled by them both until noon]

Since (1) = (3), we get 4a = bs …..(4)
Since (2) = (3), we get 9b = as …..(5)

Multiply equations (4) and (5) and get 36ab = ab s^2

So s^2 = 36,
s=6
sunrise occurs 6 hours before noon.

[snookersfun]

Do you want me to post it here?

OK, let's have the answer...

[davis_greatest]

Nobody else having a try? There is a simple answer to it.

Do you want me to post it here?

[snookersfun]

something fast for between tournaments:

2 people start traveling at sunrise, one from A to B, the second from B to A. They travel at constant speed throughout the day without taking breaks.
After meeting at noon one person arrives at B at 4pm the second at A at 9pm. At which time was sunrise on that day? (Assuming it happened at the same time for both)

Nobody else having a try? There is a simple answer to it.

[davis_greatest]

6h 42m 30s

Yes, good to see a new member on this thread. So, welcome! The answer to snookersfun's round 109 is a lot simpler than that, however!

Don't forget that round 108 is still open too!

http://www.thesnookerforum.com/showp...ount_1300.html

[Royston63]

Hi Royston63,
welcome to this thread. So, you found us, I thought you might like numbers...
About the result, I got a slightly different one, so maybe you want to recheck meanwhile (and I will maybe recheck mine, as I am known to throw in mistakes as well)!

oh yes I very likes numbers... and I haven't time now, I must go to the kitchen... thank you

[snookersfun]

6h 42m 30s

Hi Royston63,
welcome to this thread. So, you found us, I thought you might like numbers...
About the result, I got a slightly different one, so maybe you want to recheck meanwhile (and I will maybe recheck mine, as I am known to throw in mistakes as well)!

[Royston63]

6h 42m 30s

[snookersfun]

aaarrggghhhh (no problem finding 10 letters)

yes!

[davis_greatest]

I assume that their longitudinal positions at sunrise are sufficiently close that we should assume that sunrise occurs simultaneously for each of them?

[snookersfun]

Round 109

something fast for between tournaments:

2 people start traveling at sunrise, one from A to B, the second from B to A. They travel at constant speed throughout the day without taking breaks.
After meeting at noon one person arrives at B at 4pm the second at A at 9pm. At which time was sunrise on that day?

[davis_greatest]

... and please ask Charlie to describe the progress of the break.

Hehehe... something wrong with Barry's descriptions?

[davis_greatest]

Congratulations to snookersfun and abextra who both solved rounds 106 and 107. They've also both solved round 108 (by Private Message), so anyone else who completes it, post the answer on the thread please...

[abextra]

... keep them coming

... and please ask Charlie to describe the progress of the break.

[snookersfun]

oh swell, that should have been edited out by now....