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Suppose that you are a traffic-light timing expert for a medium sized city with an increasing population.  More peple meansmoredrivers, which means more traffic control devices.  Use what you learned about fractions, percents, ratios, proportions, probabilities, and decimals to solve these problems involving the timing of traffic lights.

 

A light on Washington Street is currently set at 3minutes for green, 1 minute for yellow, and 2 minutes for red for each cycle.  Write the fractions for the amount of time that thelight spends on each color during one cycle.  Be sure to write them in simplest form.

1.

 green    ______

2.

 yellow   ______

3.

 red       _______
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The light at the same intersection on Lincoln Street is green for 1 1/2 minutes, yellow for 1/2 minute, and red for 4 minutes.   Write the fractions for the amount of time in minutes that the light spends on each color for one cycle.  Be sure to write them in simplest form.

4.

 green    ______

5.

 yellow   ______

6.

 red       _______
On Sunday through Thursday the traffic lights at this intersection operate from 5:00 am until 10:00 pm.  The remander of the time, the lights flash yellow in one direction and red in the other direction.  Based on the timing ratios you calculated above, calculate the number of minutes that the lights are on each color on a Monday.  Remember to consider only the amount of time the lights are operating normally, not flashing.

7.

 Washington Street:
green   _____ yellow   _____ red   _____

8.

 Lincoln Street:
green   _____ yellow   _____ red   _____

 

On Friday and Saturday, the same traffic lights operate on the same cycle from 5:00am until midnight.  Calculate the number of minutes that the lights are each color on a Friday.

9.

 Washington Street:
green   _____ yellow   _____ red   _____

10.

 Lincoln Street:
green   _____ yellow   _____ red   _____

 

Calculate the amount of time in hours that the lights spend on each color for one week: Sunday at 5:00 am to Saturday at midnight.  Give your answer in hours and fractions of hours, not in hours and minutes.

11.

 Washington Street:
green   _____ yellow   _____ red   _____

12.

 Lincoln Street:
green   _____ yellow   _____ red   _____

 

Write the ratios for the colors of the traffic light in terms of

              number of hours on each color in one week                    number of hours operating normally(not flashing) in a week

13.

 Washington Street:
green   _____ yellow   _____ red   _____

14.

 Lincoln Street:
green   _____ yellow   _____ red   _____
Convert these ratios to percents.

15.

 Washington Street:
green   _____ yellow   _____ red   _____

16.

 Lincoln Street:
green   _____ yellow   _____ red   _____

 

The intersection is becoming busier, and the traffic light timing needs to be altered.  If the times for one cycle are altered as listed below, write the fractions for the amount of time in seconds that the light spends on each color for one cycle.  Be sure to write in simplest form.
Washington Street:
green = 5 min. yellow = 1.5 m. red = 3 min.
Lincoln Street:
green = 2 min. yellow = 1 min. red = 6.5 min.

17.

 Washington Street:
green   _____ yellow   _____ red   _____

18.

 Lincoln Street:
green   _____ yellow   _____ red   _____

 

The manager of the department of transportation and the police cheif have recomended that the intersection recieve left turn arrows on Washington Street because of the number of accidents at the intersection.  You decide to solve the problem by adding left turn arrows on Washington Street and having them green for 1/5 of the time alloted for the green light.  Adjust your ratios for Washington Street to account for this addition. 19.      green left-turn arrow_______               green_______

             yellow_______                                       red _______

 

20.   What is the probability that a person driving up            to the intersection on Lincoln Street will have a             green light? _____________________________________

 

21.     What is the probability that a person driving up             to the intersection on Washington Street will have a             green light? _____________________________________

After meeting with the city planner, you know that in the future this intersection will be expanded by increasing the number of lanes to accomodate the increase in traffic resulting from the construction of nearby shopping areas and houses.  You predict the following conditions:

  • Washington Street will have two left turn lanes in each direction that requires green, yellow, and red left-turn arrows.
  • Lincoln Street will have onr left turn lane in each direction that requires green, yellow, and red left-turn arrows.
  • The intersection will be heavily traveled and will need short cycle times to keep the cars moving fairly quickly.

 

 

22.     Given these conditions, develop a plan for how             much time a light should be on  in each direction on             each street. Remember that when the light is green             or yellow on one street, the light must be red on the             other street. ____________________________________________________

____________________________________________________

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Write the timing ratios in seconds for each light, based on the plan you developed for Exercise 22.

 

23.   Washington Street:
green left-turn arrow      ________ green light       _______
yellow left-turn arrow    ________ yellow light      _______
red left-turn arrow          ________ red light            _______

 

24.   Lincoln Street:
green left-turn arrow      ________ green light       _______
yellow left-turn arrow    ________ yellow light      _______
red left-turn arrow          ________ red light            _______

25.     Based on your plan, what is the probability that a person driving up to the intersection at Lincoln Street will             have a red light?         ___________

26.      What is the probability that a person driving up to the intersection on Washington Street will have a yellow               left-turn arrow?       ___________

27.       How many minutes during rush hour each evening will Washington Street's lights be green (not including the               left-turn arrow) if rush hour is from 4:00 pm  to 6:00 pm?     __________

28.      To access the shopping areas, acar must turn left from Washington Street to go south on Lincoln Street, turn              right to go south on Lincoln Street from Washington Street, or continue south on Lincoln Street.  The future             shop owners would like to know how many mintes per hour the lights will be green to allow the cars turning              left and cars continuing south to come to their stores.      _________

29.        A rush-hour traffic jam can create conditions in which each car requires 10 seconds to get through the                intersection at a green light.  Using your plan for the future intersection traffic-light timing, how many cars                could get through the intersection in one light cycle?    __________

30.        If these conditions lasted for 45 minutes, how many cars could get through the intersection?     ________

31.        Do you think your plan will be acceptable? Why or why not?

             _______________________________________________________________________________

             _______________________________________________________________________________

            ________________________________________________________________________________