Vol. 10 No 5 - Pi Mu Epsilon

PROBLEMS AND SOLUTIONS 43 1We may display these results in the following five regions:1. T = .85S if P > 7SA7 + 44000 and S S +36941.18 and S > 12000;2. T = .5S + .85P - 37400 if 44000 < P < 75/17 + 44000 and S 512000;3. T = .85P - 31400 if 44000 < P 5 S + 36941.18 and S > 12000;4. T = .5S if S + 32000 C P 5 44000 and S S 12000; and5. T = .5P - 16000 if P 32000. Wegraph the boundaries of these five regions into which the SP-plane isdivided. (We note there is a void region for S > 12000 and P > 44000.). Also solved by Mark Evans and the Proposer.869. [Fall 19951 Proposed by Rasoul Behboudi, University of NorthCarolina, Charlotte, North Carolina.Consider an ellipse with center at 0 and with major and minor axes ASand CD respectively. Let E and F be points on segment OB so that we haveOE2 + OF 2 = OB 2 . At E and F erect perpendiculars to cut arc BC at G362 PI MU EPSILON JOURNAL1600150014001200-a uS. 1000-c 03 weoo- BOOa002000Simulated Traffic Flow (4 cars)Figure 7.al-World ComparisonThe table below shows yellow light durations at several intersections inHope College area. As one can see, the model (which predicts minimumues for t,J for die most part agrees with actual traffic signals. Agreements andancies should not be taken too seriously, since the predictions were basedon very rough estimates of braking accelerations and intersection widths (it's hardto measure the width of an intersection when pesky cars keep getting in the way).Com~arisons with Actual Traffic LightsLocation S D Limit ~ Predicted t ;,d Actual tF,' 8' @ River 25 miyhr 3.6s 3.7s8* @ Central 25 miflu 3.6s 4.0s8th @ College 25 mih 3.6s 3.5s8th@US31 35mih.r 5.3s 6.2sUS31@8' 55mih 5.6s 4.5s9* @Central 30 mi/hr 3.7s 4.0s9' @ College 30 milhr 3.8s 4.0s