# 24 hour clock problem?

A vehicle using a 24 clock will maximize distance after
occurrences of time, (h+m+s)s accumulate, and constant
speed then after is also given by (h+m+s) m/s.

At what time does the trip end and how far did it
travel? Time starts at 00:00:00.
Update: Example: 08:14:05 yields (8+14+5) = 27 s
Update 2: Hi Fred.
Actually, at some time XX:XX:XX on the clock one
has accumulated the maximum number of time intervals,
n*27 for example, possible. One must then start the
trip at 27 m/s. To make this more physical, imagine your
electric car battery has stored maximum energy and thus
time(s) and is reading to go.
Update 3: Yes Fred. Maybe this will help: Starting the trip at 00:00:00 gives:
S = v*T = 0 m/s * (1*0)s = 0 m since there's only one occurrence, and
the same goes for 23:59:59.
Update 4: Sorry Fred, I can be alittle more clear.
For the case 23:59:59; you would start
the trip at this time and: s = vt = 141 m/s*(1*141)s
but this would not give maximum distance.
Update 5: @anyone:
Feel free to ask for more feedback. This problem has a simple solution.
It can be solved on a purely mathematical basis without reference
to physics, but speaking for myself, I find this sort of thing more
interesting with some physical basis. Thank you.
Update 6: Correct. You would then leave at 03:00:00 and the trip would end 30s after said time. Why the wait? It really doesn't matter, but let's say for some ponderable reason it took that long relative to 00:00:00 to charge your electric car battery, or maybe the gas pump flow rate was extremely low needless to... show more Correct. You would then leave at 03:00:00
and the trip would end 30s after said time.
Why the wait? It really doesn't matter, but
let's say for some ponderable reason it took
that long relative to 00:00:00 to charge your
electric car battery, or maybe the gas pump flow
rate was extremely low needless to say. Consequently,
you had some ripe words for the station owner thereby
violating the Principle of Care :)
Update 7: n= 1 v= 0 s= 0 n= 3 v= 1 s= 3 n= 6 v= 2 s= 24 n= 10 v= 3 s= 90 n= 15 v= 4 s= 240 n= 21 v= 5 s= 525 n= 28 v= 6 s= 1008 n= 36 v= 7 s= 1764 n= 45 v= 8 s= 2880 n= 55 v= 9 s= 4455 ..... n= 1290 v= 73 s= 6874410 n= 1284 v= 74 s= 7031184 n= 1276 v= 75 s= 7177500 n= 1266 v= 76 s=... show more n= 1 v= 0 s= 0
n= 3 v= 1 s= 3
n= 6 v= 2 s= 24
n= 10 v= 3 s= 90
n= 15 v= 4 s= 240
n= 21 v= 5 s= 525
n= 28 v= 6 s= 1008
n= 36 v= 7 s= 1764
n= 45 v= 8 s= 2880
n= 55 v= 9 s= 4455
.....
n= 1290 v= 73 s= 6874410
n= 1284 v= 74 s= 7031184
n= 1276 v= 75 s= 7177500
n= 1266 v= 76 s= 7312416
n= 1254 v= 77 s= 7434966
n= 1240 v= 78 s= 7544160
n= 1224 v= 79 s= 7638984
n= 1206 v= 80 s= 7718400
n= 1186 v= 81 s= 7781346
n= 1164 v= 82 s= 7826736
n= 1140 v= 83 s= 7853460
n= 1116 v= 84 s= 7874496
n= 1092 v= 85 s= 7889700
n= 1068 v= 86 s= 7898928

Wouldn't GM or Ford love to have a battery
with mucho energy density!
==> start time 23:59:05
==>end time 25.23 hr. later
==>n= 1044, t=n*87s, v= 87 m/s, s= 7902036 m

n= 1020 v= 88 s= 7898880
n= 996 v= 89 s= 7889316
n= 972 v= 90 s= 7873200
n= 948 v= 91 s= 7850388
n= 924 v= 92 s= 7820736
n= 900 v= 93 s= 7784100
n= 876 v= 94 s= 7740336
n= 852 v= 95 s= 76893
Update 8: n= 828 v= 96 s= 7630848 n= 804 v= 97 s= 7564836 n= 780 v= 98 s= 7491120 n= 756 v= 99 s= 7409556 ... n= 66 v= 131 s= 1132626 n= 55 v= 132 s= 958320 n= 45 v= 133 s= 796005 n= 36 v= 134 s= 646416 n= 28 v= 135 s= 510300 n= 21 v= 136 s= 388416 n= 15 v= 137 s= 281535 n= 10 v= 138 s=... show more n= 828 v= 96 s= 7630848
n= 804 v= 97 s= 7564836
n= 780 v= 98 s= 7491120
n= 756 v= 99 s= 7409556
...
n= 66 v= 131 s= 1132626
n= 55 v= 132 s= 958320
n= 45 v= 133 s= 796005
n= 36 v= 134 s= 646416
n= 28 v= 135 s= 510300
n= 21 v= 136 s= 388416
n= 15 v= 137 s= 281535
n= 10 v= 138 s= 190440
n= 6 v= 139 s= 115926
n= 3 v= 140 s= 58800
n= 1 v= 141 s= 19881