To compare the hiking distances, we first convert all distances to improper fractions with a common denominator.
-
First friend's distance: \(1 \frac{3}{7}\)
\[ 1 \frac{3}{7} = \frac{7 \times 1 + 3}{7} = \frac{10}{7} = \frac{40}{28} \]
-
Second friend's distance: \(1 \frac{1}{14}\)
\[ 1 \frac{1}{14} = \frac{14 \times 1 + 1}{14} = \frac{15}{14} = \frac{30}{28} \quad (\text{after scaling up to denominator 28}) \]
-
Third friend's distance: \(1 \frac{1}{4}\)
\[ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} = \frac{35}{28} \quad (\text{after scaling up to denominator 28}) \]
Now we have the distances in terms of the common denominator of 28:
- First friend: \( \frac{40}{28} \)
- Second friend: \( \frac{30}{28} \)
- Third friend: \( \frac{35}{28} \)
Now we compare these values from the largest to the smallest:
- \( \frac{40}{28} \) (1st friend)
- \( \frac{35}{28} \) (3rd friend)
- \( \frac{30}{28} \) (2nd friend)
So the numerical order of the distances hiked from most to least is:
- \( \frac{40}{28} \) (First friend: \(1 \frac{3}{7}\))
- \( \frac{35}{28} \) (Third friend: \(1 \frac{1}{4}\))
- \( \frac{30}{28} \) (Second friend: \(1 \frac{1}{14}\))
The correct order from the given responses is: 40/28 , 35/28 , 30/28 (or \(1 \frac{3}{7}, 1 \frac{1}{4}, 1 \frac{1}{14}\)).
However, none of the listed options match this order.
Thus, the correct order of hiking distances is not included in the options, but based on the conversions it should be:
- 1 3/7
- 1 1/4
- 1 1/14
So the correct order from most to least is: 1 3/7 , 1 1/4 , 1 1/14 which is 40/28 , 35/28 , 30/28 when converted to improper fractions.
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