Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?

Options

A. A) `2 9/7 km`
B. B) `3 7/5 km`
C. C) `1 3/4 km`
D. D) `4 3/8 km`

Answer

To solve the problem step by step, we need to find out how far apart two men, A and B, are after walking for 3.5 hours in the same direction.

### Step 1: Convert the speeds into improper fractions
- A's speed = 4 ½ km/h = \( \frac{9}{2} \) km/h
- B's speed = 5 ¾ km/h = \( \frac{23}{4} \) km/h

### Step 2: Calculate the relative speed
Since both A and B are walking in the same direction, we need to find the relative speed by subtracting A's speed from B's speed.
- Relative speed = Speed of B - Speed of A
- Relative speed = \( \frac{23}{4} - \frac{9}{2} \)

To perform the subtraction, we need a common denominator:
- Convert \( \frac{9}{2} \) to have a denominator of 4:
\( \frac{9}{2} = \frac{18}{4} \)

Now we can subtract:
- Relative speed = \( \frac{23}{4} - \frac{18}{4} = \frac{5}{4} \) km/h

### Step 3: Convert the time into an improper fraction
- Time = 3 ½ hours = \( \frac{7}{2} \) hours

### Step 4: Calculate the distance apart
Now, we can find the distance apart by using the formula:
- Distance = Relative speed × Time
- Distance = \( \frac{5}{4} \) km/h × \( \frac{7}{2} \) h

Calculating this gives:
- Distance = \( \frac{5 \times 7}{4 \times 2} = \frac{35}{8} \) km

### Step 5: Convert the distance into a mixed number
To convert \( \frac{35}{8} \) km into a mixed number:
- \( 35 \div 8 = 4 \) remainder \( 3 \)
- So, \( \frac{35}{8} = 4 \frac{3}{8} \) km

### Final Answer
At the end of 3.5 hours, A and B are \( 4 \frac{3}{8} \) km apart.

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