Sure, let's solve this step-by-step.
1. Data from the Problem:
- The first line of shopping carts has 10 carts and the total length is 2.9 meters.
- The second line of shopping carts has 20 carts and the total length is 4.9 meters.
2. Calculate the Length of One Cart in the First Line:
- We need to find the average length of one cart in the first line by dividing the total length by the number of carts.
- Length of one cart in the first line = Total length of the first line / Number of carts
- So, [tex]\( \text{Length of one cart in the first line} = \frac{2.9 \ \text{meters}}{10 \ \text{carts}} = 0.29 \ \text{meters} \)[/tex]
3. Calculate the Length of One Cart in the Second Line:
- Similarly, we need to find the average length of one cart in the second line by dividing the total length by the number of carts
- Length of one cart in the second line = Total length of the second line / Number of carts
- So, [tex]\( \text{Length of one cart in the second line} = \frac{4.9 \ \text{meters}}{20 \ \text{carts}} = 0.245 \ \text{meters} \)[/tex]
4. Consistent Length of One Shopping Cart:
- Ideally, the length of one shopping cart should be consistent regardless of the number of carts and the total length of the line. To find the best estimate of the length, we can calculate the average of the two lengths we obtained.
- Average length of one shopping cart = [tex]\( \frac{\text{Length of one cart in the first line} + \text{Length of one cart in the second line}}{2} \)[/tex]
- So, [tex]\( \text{Average length of one cart} = \frac{0.29 \ \text{meters} + 0.245 \ \text{meters}}{2} = 0.2675 \ \text{meters} \)[/tex]
Therefore, the length of one shopping cart, in meters, is approximately 0.2675 meters.
