# Exercise 9 – How would estimate the total number of cars that are in the Highway 101 between San Francisco and Mountain View right now?

I’ve been asked by a few users of the site to post one question per exercise to make it easier for the viewers to commit to submitting their answers. I think it’s a good idea and I’m going to start this model. Starting today, I’ll publish one exercise per post.

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Geoff

I’d go with talking or writing out your thoughts.

What is the length of highway between SF and Mountainview? How wide is the highway?
A: ~40 miles, 4 lanes wide in each direction

What time of day are we talking about or is it the average of all hours in the day? Rush hour is more compact, 1am is less compact…for this example, let’s assume that the road is 40% full of vehicles (that’s crowded, btw…given that there has to be some buffer space between vehicles).
A: 40% of the 40 miles is occupied by cars (call out that this is a potential area for error that you might need to tweak)

What is the average length of a car?
A: 15ft (guesstimate)

Okay, so now for some math…let’s figure out a 1 mile section to keep it easy.
In 1 mile (5,280ft) of highway, if you had 100% density, how many cars would you be able to fit in one lane? 5280 feet / 15 feet = 352 cars with zero space between them

Now spread them out (apply the 40% density): 352 cars * 40% = 140 cars

Now multiply by 8 lanes (4 in each direction): 140 cars x 8 lanes = 1120 cars

With that number, go ahead and multiply by the 40 miles of road between Mountainview and SF: 1120 cars x 40 miles = 44,800 cars