Two school vans start from a house at an interval of 8 minutes and travel with a speed of 25km/hr. With how much speed (km/hr) should a woman coming from the opposite direction towards the house travel. To meet the vans at an interval at of 4 minutes ?

Options

A. A) 25
B. B) 27
C. C) 26
D. D) 24

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the problem
Two school vans start from a house at an interval of 8 minutes and travel at a speed of 25 km/hr. A woman is coming from the opposite direction and needs to meet the vans at an interval of 4 minutes. We need to find the speed of the woman.

### Step 2: Define the variables
Let the speed of the woman be \( x \) km/hr.

### Step 3: Calculate the distance traveled by the vans
The distance traveled by the first van in 8 minutes can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The speed of the van is 25 km/hr, and we need to convert 8 minutes into hours:
\[ 8 \text{ minutes} = \frac{8}{60} \text{ hours} = \frac{2}{15} \text{ hours} \]
Now, calculate the distance:
\[ \text{Distance} = 25 \times \frac{2}{15} = \frac{50}{15} = \frac{10}{3} \text{ km} \]

### Step 4: Calculate the distance traveled by the woman
The woman meets the first van after 4 minutes. Convert 4 minutes into hours:
\[ 4 \text{ minutes} = \frac{4}{60} \text{ hours} = \frac{1}{15} \text{ hours} \]
The distance traveled by the woman in this time is:
\[ \text{Distance} = x \times \frac{1}{15} \text{ km} \]

### Step 5: Set up the equation
Since the distance covered by the first van in 8 minutes is equal to the distance covered by the woman in 4 minutes, we can set up the equation:
\[ \frac{10}{3} = x \times \frac{1}{15} \]

### Step 6: Solve for \( x \)
To solve for \( x \), multiply both sides by 15:
\[ 15 \times \frac{10}{3} = x \]
This simplifies to:
\[ x = 15 \times \frac{10}{3} = 50 \text{ km/hr} \]

### Step 7: Conclusion
The speed of the woman should be 50 km/hr.