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amm1812
1 month ago
9

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 tr

avel 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?
Mathematics
1 answer:
Svet_ta [12.7K]1 month ago
7 0

Answer:

1,200 cars per hour

Step-by-step explanation:

Assuming a steady flow of vehicles, as noted in the scenario.

If we imagined a counter at your position, there would be 25 cars within a quarter-mile, including your vehicle, all traveling at your speed.

Next, let's determine how long it takes to cover that quarter-mile distance. With your velocity at 60 mph, we can set up a proportion:

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

¼ of a mile --------> x hours

Then we can calculate:

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

This indicates that in 1/240 hours, all 25 cars pass by the counter.

Now, let's find how many cars pass the counter in one hour. By cross-multiplying, we get:

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

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

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

The highway's flow rate in the direction you are heading is 1,200 cars per hour.

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