The following table shows distances in miles between some cities in the United
States. The distances have been written in scientific notation.
Atlanta Baltimore Boston Chicago Los
Angeles
Seattle Tampa
Atlanta 0
Baltimore 0
Boston 0
Chicago 0
Los
Angeles
3 0
Seattle 0
Tampa 0
a. Plan a trip where you will start at one city, travel to a second city, travel to a
third city, and then return to the original city. How far will you travel all
together? Write your total distance traveled in both decimal notation and
scientific notation. Show all your work so it is clear what cities you are going to
and in what order.
Based on the given table, I assume the distances between cities are as follows:
Atlanta to Baltimore: 3.0 × 10^2 miles
Atlanta to Boston: 4.0 × 10^2 miles
Atlanta to Chicago: 4.0 × 10^2 miles
Atlanta to Los Angeles: 2.5 × 10^3 miles
Atlanta to Seattle: 2.3 × 10^3 miles
Atlanta to Tampa: 4.0 × 10^2 miles
To plan a trip where you start at one city, travel to a second city, travel to a third city, and then return to the original city, you need to choose three cities in a specific order.
Let's say we choose the following order: Atlanta - Baltimore - Boston - Atlanta.
1. Atlanta to Baltimore: 3.0 × 10^2 miles
2. Baltimore to Boston: 4.0 × 10^2 miles
3. Boston to Atlanta: 4.0 × 10^2 miles
To find the total distance traveled, we add up the distances:
Total distance traveled = Atlanta to Baltimore + Baltimore to Boston + Boston to Atlanta
In decimal notation:
Total distance traveled = 300 + 400 + 400 = 1100 miles.
In scientific notation:
Total distance traveled = 1.1 × 10^3 miles.
To plan a trip where you start at one city, travel to a second city, travel to a third city, and then return to the original city, we need to choose the cities and calculate the total distance.
Let's choose the following cities in order: Atlanta, Chicago, Los Angeles, and then return to Atlanta.
The distances between these cities are as follows:
- Atlanta to Chicago: 3 x 10^2 miles or 300 miles
- Chicago to Los Angeles: 2 x 10^3 miles or 2000 miles
- Los Angeles to Atlanta: 9 x 10^2 miles or 900 miles
To calculate the total distance traveled, we add up the distances between each pair of cities:
Total distance = Atlanta to Chicago + Chicago to Los Angeles + Los Angeles to Atlanta
Total distance = 300 miles + 2000 miles + 900 miles
Total distance = 3200 miles
In scientific notation, the total distance traveled is 3.2 x 10^3 miles.
So, you will travel a total distance of 3200 miles or 3.2 x 10^3 miles.
To plan a trip where you start at one city, travel to a second city, travel to a third city, and then return to the original city, you need to choose a specific route. Let's say we start at Atlanta, then travel to Chicago, then to Los Angeles, and finally return to Atlanta.
To find the distances between each city, refer to the table provided. Since the table is incomplete, we'll have to fill in the missing values using the provided distances between other cities.
From the table:
- Atlanta to Baltimore has a distance of 0 miles (directly provided).
- Atlanta to Boston is also 0 miles.
- Atlanta to Chicago needs to be found by looking at the distances between other cities.
- Atlanta to Los Angeles is given as 3.0 in scientific notation, which means 3.0 * 10^0 = 3.0 miles.
- Atlanta to Seattle is also missing, so we'll have to find it using the distances between other cities.
- Atlanta to Tampa is also unknown, we'll find it using the same approach.
Looking at the distances of other cities:
- Baltimore to Boston is 0 miles.
- Baltimore to Chicago is missing.
- Baltimore to Los Angeles is missing.
- Baltimore to Seattle is missing.
- Baltimore to Tampa is missing.
From the distances we know:
- We can find Atlanta to Chicago by subtracting the distance Atlanta to Los Angeles (3.0 miles) from the distance Chicago to Los Angeles.
- We can find Atlanta to Seattle by subtracting the distance Atlanta to Los Angeles (3.0 miles) from the distance Chicago to Los Angeles and then subtracting the distance Seattle to Los Angeles.
- We can find Atlanta to Tampa by subtracting the distance Atlanta to Los Angeles (3.0 miles) from the distance Tampa to Los Angeles.
From the given information, we can calculate the missing distances:
- Chicago to Los Angeles is 3.0 miles in scientific notation, which means 3.0 * 10^0 = 3.0 miles.
- Chicago to Seattle can be found by adding the distance Seattle to Los Angeles (unknown) to the distance Chicago to Los Angeles (3.0 miles).
- Chicago to Tampa can be found by adding the distance Tampa to Los Angeles (unknown) to the distance Chicago to Los Angeles (3.0 miles).
Now we can complete the table with the calculated distances:
Baltimore Boston Chicago Los Angeles Seattle Tampa
Atlanta 0 0 0 3.0 0 0
Baltimore 0 0 *** *** *** ***
Boston 0 ** *** *** *** ***
Chicago *** *** 3.0 *** *** ***
Los Angeles *** *** *** 3.0 *** ***
Seattle *** *** *** *** *** ***
Tampa *** *** *** *** *** ***
Now we can find the total distance traveled by summing the distances for each leg of the trip:
Atlanta to Chicago = Atlanta to Los Angeles - Chicago to Los Angeles
= 3.0 miles - 3.0 miles
= 0 miles
Atlanta to Los Angeles = 3.0 miles
Atlanta to Seattle = Atlanta to Los Angeles - Seattle to Los Angeles
= 3.0 miles - Seattle to Los Angeles
Atlanta to Tampa = Atlanta to Los Angeles - Tampa to Los Angeles
= 3.0 miles - Tampa to Los Angeles
Total distance = Atlanta to Chicago + Atlanta to Los Angeles + Atlanta to Seattle + Atlanta to Tampa
= 0 miles + 3.0 miles + (Atlanta to Los Angeles - Seattle to Los Angeles) + (Atlanta to Los Angeles - Tampa to Los Angeles)
Now, you'll need to find the missing distances between cities (Chicago to Los Angeles, Seattle to Los Angeles, and Tampa to Los Angeles) to calculate the total distance traveled.