Question

(b) (i)
Hawa walked two fifth of her journey, John walked three eighth of his journey. If these two people have the same length of their journey, who walked the shortest distance?

Answer 1

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 \( D \):

1. **Hawa's Distance**:
\[
\text{Distance Hawa walked} = \frac{2}{5}D
\]

2. **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:
- For Hawa:
\[
\frac{2}{5}D = \frac{2 \times 8}{5 \times 8}D = \frac{16}{40}D
\]

- 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.