A Chess Christmas Quiz

You mean HOLIDAY Quiz right?

No. I've retired, everyday is a holiday.

It maybe a wee bit early. (the supermarkets had their Christmas trees up
in the first week of November and started piping out the Christmas tunes).
But soon I am going on a month long complete techno detox - no net, TV or phone..

This is easy once you know how these things work but it might cause some amusement to the uninitiated.
I have a daily mensa puzzle calendar and this was on it yesterday:-
Santa's elves set off to deliver presents to santa from the toy factory.
Their sleigh travels at a constant speed of 45 mph.
However one elf is late and sets off 8 minutes later at a constant speed of 60 mph.
Both follow exactly the same route.
How long will it take the lone elf to catch up with the rest?

@venda said
This is easy once you know how these things work but it might cause some amusement to the uninitiated.
I have a daily mensa puzzle calendar and this was on it yesterday:-
Santa's elves set off to deliver presents to santa from the toy factory.
Their sleigh travels at a constant speed of 45 mph.
However one elf is late and sets off 8 minutes later at a constant speed of 60 m ...[text shortened]...
Both follow exactly the same route.
How long will it take the lone elf to catch up with the rest?

45t = 60(t - 8/60)
8 = 15t
t = 8/15 hours = 32 minutes total time
2nd elf takes 24 minutes once he starts.

@bigdoggproblem said
45t = 60(t - 8/60)
8 = 15t
t = 8/15 hours = 32 minutes total time
2nd elf takes 24 minutes once he starts.

Correct.There's more than one way to tackle it but your way is probably the simplest.
I did it with ratio's the times being in the ratio of 3:4, therefore
4x =3(x +8)
x = 24

This is how my simple mind views it: (doing this in my head here)

45 mph=3/4 mp(minute) and 60 mph=1 mpm; difference = 60-45=15 mph = 1/4 mpm

8 minutes at 3/4 mpm = 6 miles head start.

It takes 4x6 = 24 minutes to go 6 miles at 1/4 mpm difference

24 minutes

As I said earlier, there's always more than 1 way to attack these sort of problems.
Thanks for your interest and imput