Today from Bedtime Math: Giving the Green Light

Try this fun math challenge with your kids!

When we drive on the road, we can't all just go every which way. We have to stay on one side, and wait our turn where roads cross. Stop signs help, but really busy crossings need traffic lights. The traffic light, that cute red, yellow and green trio, was patented (made official as an invention) on November 20th, 1923. Actually, the very first electric traffic light was invented in 1912 by Lester Wire, a policeman in Utah fed up with all the traffic; you can imagine, after hundreds of years of slow horse-drawn carriages, what it was like to have this speedy, loud thing called a car suddenly show up. So Wire borrowed the idea of railroad signals to make a traffic light, which had just red and green for stop and go. Then in 1920, Detroit cop William Potts built one with 3 colors (red, orange and green). As you see here, people have tried other designs, like this funny dial one from Australia, but the three-color light is what keeps most of us from crashing into each other today.

Now here's today's math~

Wee ones: If a traffic light has a red light, a yellow, a green, and then a green left-turn arrow, how many lights does it have?

Little kids: Lester Wire's light had 4 sides with a red and green light on each side. How many lights was that in total?  Bonus:Potts then built one with 3 colors on each of 4 sides. How many lights did that have?

Big kids: Most lights stay on red for only about 15 seconds, but some lights take forever. If the traffic light for your direction signal spends 15 seconds on green, 5 seconds on yellow, and 30 seconds on red, how long is a full cycle of green to yellow to red?  Bonus: If 8 cars can get through the green each time, how many cars make it through the light in 5 minutes? (Reminder: a minute has 60 seconds.)

The sky's the limit: If in 1 busy minute 50 cars reach a crossing from the east, 44 from the west, 12 from the north and 19 from the south, and 1 car per second can get through a green in each direction, how many cars are waiting in total after that minute if the light is green for east-west twice as much as for north-south? (Assume "green" includes the yellow warning time, and that the switch to red is simultaneous with the switch to green for the crossing traffic).

 

 

 

 

 

Answers:

Wee ones: 4 lights.

Little kids: 8 lights in total.  Bonus: 12 lights in total.

Big kids: 50 seconds.  Bonus: 48 cars. 5 minutes is the same as 300 seconds, so exactly 6 cycles will fit, no matter which light was on at the start.

The sky's the limit: 14 cars total. There are 94 cars running east-west and 31 running north-south, and every second 2 cars total will fit through (1 in each direction). The light will be green for 40 seconds for east-west, which will process 80 of those cars, leaving 14 still waiting. And for the north-south folks, the 20 seconds of green allows 40 cars, so there won't be any waiting at all. So they should reset the lights to give east-west more green time!