To determine who walked the shortest distance, we first need to express the distances Hawa and John walked in a comparable way based on the lengths of their journeys.
Let the total length of Hawa's journey be represented as \( H \) and the total length of John's journey as \( J \).
According to the problem:
- Hawa walked \( \frac{2}{5}H \)
- John walked \( \frac{3}{8}J \)
Since they have the same length of their journeys, we can set \( H = J \).
Step 1: Use \( H = J \)
Let’s denote the journey length as \( D \) (where \( D = H = J \)). Hence:
- Hawa walked \( \frac{2}{5}D \)
- John walked \( \frac{3}{8}D \)
Step 2: Compare the distances walked
Now we calculate the distances Hawa and John walked in terms of \( D \):
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Hawa's Distance: \[ \text{Distance Hawa walked} = \frac{2}{5}D \]
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John's Distance: \[ \text{Distance John walked} = \frac{3}{8}D \]
Step 3: Find a common denominator to compare
To compare \( \frac{2}{5}D \) and \( \frac{3}{8}D \), we can find a common denominator. The least common multiple of 5 and 8 is 40.
Converting each fraction:
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For Hawa: \[ \frac{2}{5}D = \frac{2 \times 8}{5 \times 8}D = \frac{16}{40}D \]
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For John: \[ \frac{3}{8}D = \frac{3 \times 5}{8 \times 5}D = \frac{15}{40}D \]
Step 4: Compare the two distances
Now we can compare:
- Hawa's distance: \( \frac{16}{40}D \)
- John's distance: \( \frac{15}{40}D \)
Since \( \frac{16}{40}D > \frac{15}{40}D \), we find that:
- Hawa walked more distance than John.
Conclusion
Thus, John walked the shortest distance.
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