Internet Table-Top Rally Championship 1998
Route Card 11 Solution

From TC11 (In) @ Bridge (4808), go via SH93, SH73, A3066, A30 leaving the map in GS 4913. Rejoin the map on the A372 in GS4925.

TC11 (Out) @ Xroads (GS4725)
TC12 (In) @ YR (GS4126)

tracom.gif (10602 bytes) In carrying out a recce on this map I used a variant of TRACOM and discovered that the time to travel a certain distance over a road colour was related exactly to the following factors:

a) Road colour. The average speed that could be achieved on White roads was 'x' kilometres per hour (kph). On Yellow roads it was (x + 10) kph. On Orange roads it was (x + 20) kph. On Red roads it was (x + 30) kph.

b) Crossing an Easting Grid Line

c) Crossing a Northing Grid line

d) Over/Under a Bridge

e) Crossing a Gradient Arrow

f) Crossing a Spot Height

g) Passing a Public Telephone

h) Passing a Milestone

I took 8 samples and came up with the following table:

Road Colour Distance (Km) b c d e f g h Time
m:ss
W 1.5 1             2:09
Y 2.2 4             3:00
O 1.3 3 3           2:39
R 2.5 1 1 7         2:57
W 1.8 2 6 5 2       5:24
Y 2.75 2 4 3 1 5     5:36
O 3.25 1 2 3 4 5 6   6:44
R 3.0 2 1 2 3 1 2 4 5:30

The distances were measured as the "Crow" flies from the junction at the start of the section to the junction at the finish of the section. Measurement was rounded to the nearest 0.25 kilometres.

For example. I travelled a section of just Yellow roads which was measured (as above) as 2.75 km. During the course of the yellow roads I crossed 2 eastings, 4 Northings, 3 Bridges, 1 Gradient Arrow and 5 Spot heights, and it took me 5 minutes 36 seconds.

From this table I worked out that there was a different delay of a whole number of seconds caused by visiting each feature b) to h), and x was a positive whole number for the kilometres per hour.

I then used the values to calculate how long each section on this route card would take, and came up with the following answers (in minutes:seconds).

3:26    (?RC1)    2:10     (?RC2)    1:29    (?RC3)    3:21     (?RC4)    2:11    (?RC5)    0:32     (?RC6)    1:30    (?RC7)    1:05     (?RC8)    3:48    (?RC9)    1:53     (?RC10)    1:29

So there were 21 sections in total, each one using just a single road colour. Where the travelling time did not calculate as a whole number of seconds, I rounded down to the previous second. For example, if x = 48 mph, and I travelled 2.25 kms on white roads, this computes to 168.75 seconds (2.25 * 3600 / 48) so I will have used 168 seconds.

For each of the 10 ?s, discover the route and calculate how long that section should have taken based upon my formulae, and record the answers (in minutes and whole seconds) for your Route Checks. For every second that you deviate from the correct answer you will lose 0.1 marks up to a maximum of 1 mark per Route Check.



Solving the first part of the route card (by simultaneous equations, spreadsheet or multi-dimensional graph paper) yielded the following values: x = 45 kph, b = 9 secs, c = 20 secs, d = 4 secs, e = 11 secs, f = 7 secs, g = 14 secs, h = 18 secs The route sections were constructed as follows:

Road
Colour

Actual
Distance
Rounded
Distance

Travel
Time
(secs)

b c d e f g h

Total
Time
(secs)

Total
Time
m:ss

RC
Y 2.32 2.25 147 2 1     1 1   206 3:26  
W 2.75 2.75 220 3 1 1   2     285 4:45 1
O 1.46 1.50 83   2     1     130 2:10  
Y 0.43 0.50 32               32 0:32 2
W 1.00 1.00 80 1             89 1:29  
Y 1.30 1.25 81 1 1     1     117 1:57 3
R 2.40 2.50 120 2 1 1   1 1 1 194 3:21  
O 1.45 1.50 83 2       1     108 1:48 4
Y 1.60 1.50 98 1 1 1         131 2:11  
W 0.56 0.50 40   1 1         64 1:04 5
Y 0.52 0.50 32               32 0:32  
O 1.97 2.00 110 2 1     1     155 2:35 6
Y 1.34 1.25 81 1             90 1:30  
W 0.62? 0.50 40 1 1           69 1:09 7
Y 0.79 0.75 49 1       1     65 1:05  
W 0.85 0.75 60               60 1:00 8
Y 2.60 2.50 163 3 1   1 1     228 3:48  
R 1.75 1.75 84 2 2 2   1     157 2:37 9
W 1.27 1.25 100 1   1         113 1:53  
Y 2.61 2.50 163 2 3 2   1     256 4:16 10
R 1.19 1.25 60 1 1           89 1:29  

It was possible that the white in RC7 could have been 0.625+km, so I allowed answers of 1:09 or 1:29.