TADM2E 1.3 - Revision history

Matt: Undo revision 839 by Ufsuraifs (talk)

2020-07-23T14:45:25Z

Undo revision 839 by Ufsuraifs (talk)

Ufsuraifs: Blanked the page

2020-07-17T02:53:20Z

Blanked the page

Anand at 07:32, 12 September 2015

2015-09-12T07:32:34Z

Zapstar: Corrected the graph figure.

2015-09-11T15:37:23Z

Corrected the graph figure.

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2014-09-11T18:22:28Z

Recovering wiki

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2014-09-11T18:13:11Z

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New page

a ----------- c ----------- b
\ /
\--------- d ---------- /

If the distance from ''a'' to ''b'' going through ''d'' is less than the distance from ''a'' to ''b'' going through ''c'' but there is a busy traffic intersection at ''d'' with a stop sign that is always backed up, then the route from ''a'' to ''b'' through ''c'' is faster, but the route through ''d'' is shorter.

For example,

<math>dist(a, c) = 10</math> miles

<math>dist(c, b) = 5</math> miles

So the distance from ''a'' to ''b'' through ''c'' is 15 miles. Assuming you drive 30 miles per hour, the time to travel this would be 30 minutes

<math>dist(a, d) = 5</math> miles

<math>dist(c, b) = 5</math> miles

So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.

[[introduction-TADM2E|Back to ''Introduction ...'']]

← Older revision		Revision as of 02:53, 17 July 2020
Line 1:		Line 1:
−	~~a ----------- c ----------- b~~
−	~~\ /~~
−	~~\--------- d ---------- /~~

−	If the distance from ''a'' to ''b'' going through ''d'' is less than the distance from ''a'' to ''b'' going through ''c'' but there is a busy traffic intersection at ''d'' with a stop sign that is always backed up, then the route from ''a'' to ''b'' through ''c'' is faster, but the route through ''d'' is shorter.
−
−
−	~~For example,~~
−
−	~~<math>dist(a, c) = 10</math> miles~~
−
−	~~<math>dist(c, b) = 5</math> miles~~
−
−	~~So the distance from ''a'' to ''b'' through ''c'' is 15 miles. Assuming you drive 30 miles per hour, the time to travel this would be 30 minutes~~
−
−
−	~~<math>dist(a, d) = 5</math> miles~~
−
−	~~<math>dist(c, b) = 5</math> miles~~
−
−	So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.
−
−	~~---~~
−
−	Another possible solution: You have a longer route with a higher speed and a shorter route with a lower speed. By choosing the numbers appropriately, you can make the longer route be the winner. The speed may be due to law, or due to traffic jam, or because of pot holes on the road :-)
−
−	Suppose road of length l1 has speed limit s1 and another road of length l2 has speed limit l2. The shorter route is determined by comparing l1 with l2. The faster route is determined by comparing l1/s1 with l2/s2. With positive numbers, if l1 > l2 but l1 < l2 * s1 / s2, then the faster route differs from the shorter route.
−
−
−	~~[[introduction-TADM2E\|Back to ''Introduction ...'']]~~

← Older revision		Revision as of 07:32, 12 September 2015
Line 20:		Line 20:

	So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.		So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.
		+
		+	---
		+
		+	Another possible solution: You have a longer route with a higher speed and a shorter route with a lower speed. By choosing the numbers appropriately, you can make the longer route be the winner. The speed may be due to law, or due to traffic jam, or because of pot holes on the road :-)
		+
		+	Suppose road of length l1 has speed limit s1 and another road of length l2 has speed limit l2. The shorter route is determined by comparing l1 with l2. The faster route is determined by comparing l1/s1 with l2/s2. With positive numbers, if l1 > l2 but l1 < l2 * s1 / s2, then the faster route differs from the shorter route.


	[[introduction-TADM2E\|Back to ''Introduction ...'']]		[[introduction-TADM2E\|Back to ''Introduction ...'']]

← Older revision	Revision as of 14:45, 23 July 2020
Line 1:	Line 1:
	+	a ----------- c ----------- b
	+	\ /
	+	\--------- d ---------- /

	+	If the distance from ''a'' to ''b'' going through ''d'' is less than the distance from ''a'' to ''b'' going through ''c'' but there is a busy traffic intersection at ''d'' with a stop sign that is always backed up, then the route from ''a'' to ''b'' through ''c'' is faster, but the route through ''d'' is shorter.
	+
	+
	+	For example,
	+
	+	<math>dist(a, c) = 10</math> miles
	+
	+	<math>dist(c, b) = 5</math> miles
	+
	+	So the distance from ''a'' to ''b'' through ''c'' is 15 miles. Assuming you drive 30 miles per hour, the time to travel this would be 30 minutes
	+
	+
	+	<math>dist(a, d) = 5</math> miles
	+
	+	<math>dist(c, b) = 5</math> miles
	+
	+	So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.
	+
	+	---
	+
	+	Another possible solution: You have a longer route with a higher speed and a shorter route with a lower speed. By choosing the numbers appropriately, you can make the longer route be the winner. The speed may be due to law, or due to traffic jam, or because of pot holes on the road :-)
	+
	+	Suppose road of length l1 has speed limit s1 and another road of length l2 has speed limit l2. The shorter route is determined by comparing l1 with l2. The faster route is determined by comparing l1/s1 with l2/s2. With positive numbers, if l1 > l2 but l1 < l2 * s1 / s2, then the faster route differs from the shorter route.
	+
	+
	+	[[introduction-TADM2E\|Back to ''Introduction ...'']]

@@ Line 1: / Line 1: @@
-a ----------- c ----------- b
+   a ----------- c ----------- b
      \                         /
       \--------- d ---------- /

@@ Line 8: / Line 8: @@
 For example,
-&lt;math&gt;dist(a, c) = 10&lt;/math&gt; miles
+<math>dist(a, c) = 10</math> miles
-&lt;math&gt;dist(c, b) = 5&lt;/math&gt; miles
+<math>dist(c, b) = 5</math> miles
 So the distance from ''a'' to ''b'' through ''c'' is 15 miles. Assuming you drive 30 miles per hour, the time to travel this would be 30 minutes
-&lt;math&gt;dist(a, d) = 5&lt;/math&gt; miles
+<math>dist(a, d) = 5</math> miles
-&lt;math&gt;dist(c, b) = 5&lt;/math&gt; miles
+<math>dist(c, b) = 5</math> miles
 So the distance from ''a'' to ''b'' through ''d'' is 10 miles. Assuming you drive 30 miles per hour, the time to travel this would be 20 minutes, but due to the busy intersection at ''d'', you are delayed 15 minutes, the total time would be 35 minutes.