Gallery Problems Exercise

Traffic

Work Time

Traffic

Situation A:

Monique stands by the highway. She notices that one car goes by every second. She knows that these cars are going 60 miles per hour.

  1. How many feet apart are the cars?
  2. How many cars are there on 1 mile of highway?

Justify your answers mathematically.

  • Think about 60 miles per hour as a ratio of 60 miles to 1 hour. Use this ratio to write a proportion that you could use to calculate the distance the car travels each minute and second.

  • Remember, there are 5,280 feet per mile.

Situation B:

One car goes by every second, but the cars are going 30 miles per hour.

  1. How many feet apart are the cars?
  2. How many cars are there on 1 mile of highway?

Justify your answers mathematically.

  • When the cars are traveling more slowly, what would happen to the distance between each car? How can you use the relationship between the speeds and the answer to Question 1 to help you calculate the distance between each car?

  • If you are still seeing a car every second and the cars are traveling more slowly than before, would there be more or less cars along a given length of the highway? How can you use the relationship between the speeds and the answer to Question 1 to help you calculate the number of cars on the 1-mile stretch of highway?

Situation C:

One car goes by every 2 seconds and the cars are going 75 miles per hour.

  1. How many feet apart are the cars?
  2. How many cars are there on 1 mile of highway?

Justify your answers mathematically.

  • How does the increase in time from 1 second to 2 seconds affect the problem?

  • How does this increase in time affect the distance between each car?

  • How does the increase in time affect the number of cars on the road?

  • How can you use the relationship between the original speed and the increased speed to help you calculate your answer?