You are travelling at a constant speed along a road. There are 5 sets of traffic lights along this road, and they all start their sequence at the same time as you pass the zero mile marker.

At what speed do you need to travel in order to remain at your constant speed?

traffic light 1 at 3 miles is red for 36 secs and green for 22 secs.
traffic light 2 at 4 miles is red for 28 secs and green for 40 secs.
traffic light 3 at 6 miles is red for 41 secs and green for 17 secs.
traffic light 4 at 7 miles is red for 62 secs and green for 15 secs.
traffic light 5 at 9 miles is red for 46 secs and green for 25 secs.

Note, the speed is an integer, above 25 and below 100MPH.

Problem : Traffic Calming

Ans:  To get the green signal at first traffic light, one needs to cross the same during 36th to 58th seconds or 94rth to 116th Seconds or 152th to 174th Seconds or 210th to 232th Seconds.

The above range gives us the Maximum and Minimum velocities in each range. For eg for 210 - 232 Seconds the Vmin = 46 mph and Vmax = 51 mph. (V = d /t)

From every range of integer velocities, we can obtain the time at which the vehicle will cross these five traffic lights.  Based on periodic cycle of every traffic light (Red/Green), the status of particular signal can be find out at that time.

At the speed of 47 mph, vehicle can cross TL1(traffic light one) at 229th seconds and subsequently TL2 at 306 Seconds, TL3 at 459 Seconds and TL4 at 536 seconds and lastly TL5 at 689 Seconds. At all these moments, vehicle will come across green signal and hence can pass through all five traffic lights at constant speed of 47 mph.

The Answer is 47 Miles per Hour.

Posted by vivek on 2005-02-28 08:04:25