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. Assuming you could travel the direct straight-line distance between each pair of cities, 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. Sita lives in Los Angeles, and her grandmother lives in Seattle. Sita plans to visit her grandmother three times in the next year. Assuming she travels the direct straight-line distance between the cities on each trip, what is the total distance she will travel to make these three trips? Write and evaluate an expression that uses multiplication to calculate the total distance traveled. Give your answer in both decimal notation and scientific notation. Using the table of distances, make up your own word problem that would require someone to use division to solve. Write the problem, and provide the solution.
City A: Los Angeles
City B: Seattle
Trip 1: Los Angeles to Seattle
Trip 2: Seattle to Los Angeles
Trip 3: Los Angeles to Seattle
To calculate the total distance traveled, we need to find the straight-line distance between Los Angeles and Seattle, and then multiply it by the number of trips.
Using the table of distances, we find that the distance between Los Angeles and Seattle is 1,130 miles.
Total distance traveled = 1,130 miles/trip * 3 trips
= 3,390 miles
In decimal notation, the total distance traveled is 3,390 miles.
In scientific notation, the total distance traveled is 3.39 x 10^3 miles.
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Word problem using division:
Liam is planning a road trip and wants to visit 4 cities. He has a total of 600 miles to drive, and he wants to drive an equal distance between each city. How many miles should he drive between each city?
Solution:
To find the distance Liam should drive between each city, we need to divide the total distance (600 miles) by the number of gaps between cities (4-1 = 3 gaps).
Distance between each city = 600 miles / 3 gaps
= 200 miles per gap
Liam should drive 200 miles between each city.
To plan a trip where you start in Los Angeles, travel to a second city, travel to a third city, and then return to Los Angeles, we will consider the cities in the following order: Los Angeles, Seattle, and then back to Los Angeles.
The straight-line distance between Los Angeles and Seattle can be found using the haversine formula or through an online map service. Let's assume it is 1,130 miles.
Since Sita plans to visit her grandmother three times, we will multiply the distance between Los Angeles and Seattle by 3 to find the total distance she will travel.
Total distance traveled = 1,130 miles * 3 = 3,390 miles
In decimal notation, the total distance traveled is 3,390 miles. In scientific notation, it can be written as 3.39 x 10^3 miles.
As for a word problem using division, consider the following example:
Problem: A delivery truck traveled a total distance of 300 miles and made 5 stops along the way. If the distance between each consecutive stop is the same, how far apart are the stops?
Solution:
To find the distance between consecutive stops, we can divide the total distance traveled by the number of stops made.
Distance between each consecutive stop = Total distance traveled / Number of stops
= 300 miles / 5 stops
= 60 miles
Therefore, the stops are 60 miles apart.
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 the cities you want to visit. Let's say you decide to start in Los Angeles, then travel to Seattle, then to Chicago, and finally return to Los Angeles.
To calculate the total distance traveled, you need to know the direct straight-line distance between each pair of cities. Let's assume the distances are as follows:
- Los Angeles to Seattle: 1,500 miles
- Seattle to Chicago: 1,800 miles
- Chicago to Los Angeles: 2,000 miles
To calculate the total distance traveled, you simply add up the distances between each pair of cities:
Total distance = Los Angeles to Seattle + Seattle to Chicago + Chicago to Los Angeles
= 1,500 + 1,800 + 2,000
= 5,300 miles
So, the total distance traveled is 5,300 miles.
In scientific notation, 5,300 can be written as 5.3 x 10^3, where 10^3 represents multiplying 5.3 by 1,000.
Now, let's calculate the total distance Sita will travel to make her three trips to her grandmother's house in Seattle. Assuming the direct straight-line distance between Los Angeles and Seattle is 1,500 miles, the total distance will be:
Total distance = 1,500 (distance between Los Angeles and Seattle) x 3 (number of trips)
= 4,500 miles
So, the total distance Sita will travel over the three trips is 4,500 miles.
In scientific notation, 4,500 can be written as 4.5 x 10^3, where 10^3 represents multiplying 4.5 by 1,000.
Now, let's create a word problem that requires division to solve:
Problem: A bakery produces 10,000 cookies in a day. If they want to package the cookies equally into 500 boxes, how many cookies will be in each box?
Solution: To solve this problem, we divide the total number of cookies (10,000) by the number of boxes (500).
Number of cookies per box = 10,000 ÷ 500
= 20
So, there will be 20 cookies in each box.