Question

While driving home for the holidays, you can’t seem to get Little’s Law out of your mind. You note that your average speed of travel is about 60 miles per hour. Moreover, the traffic report from the WXPN traffic chopper states that there is an average of 24 cars going in your direction on a one-quarter mile part of the highway. What is the flow rate of the highway (going in your direction) in cars per hour?

Answer 1

Answer:

1,200 cars per hour

Step-by-step explanation:

Let's suppose the car flow is constant and based on the observations stated in the problem.

If we set and imaginary car counter where your car is, then there are 25 cars in ¼ of a mile (including yours) going at your same speed.

Now compute how long it will take to travel ¼ mile. As your speed is constant 60 mph, we can cross multiply  

60 miles -----------> 1 hour

¼ of a mile --------> x hours

and

60/ (¼) = 1/x ---------> x = 1/240 hours.

This means that in 1/240 hours the 25 cars will be passing the counter.

Now compute how many cars will pass through our counter in 1 hour. Again, cross multiplying

1/240 hours -------> 25 cars

1 hour --------------> x cars

and

1/240 = 25/x -------> x = 25*240 = 1,200 cars.

So, the flow rate of the highway (going in your direction) in cars per hour is 1,200 cars per hour.