Question

Car A Is moving at a speed of 45 km/h towards car B which is moving towards car B at a speed of 55 km/h ,if the two cars were initially separated at a distance of 150m determine how long it will take the two cars to meet

Answer 1

To determine how long it will take for the two cars to meet, we first need to find their relative speed. Since both cars are moving towards each other, we can add their speeds together.

1. **Convert speeds to meters per second (m/s)** because the distance is given in meters (1 km/h = \( \frac{1000 \text{ m}}{3600 \text{ s}} \)):
- Car A: \( 45 \text{ km/h} = \frac{45 \times 1000}{3600} = 12.5 \text{ m/s} \)
- Car B: \( 55 \text{ km/h} = \frac{55 \times 1000}{3600} \approx 15.28 \text{ m/s} \)

2. **Calculate the relative speed**:
\[
\text{Relative speed} = 12.5 \text{ m/s} + 15.28 \text{ m/s} \approx 27.78 \text{ m/s}
\]

3. **Use the formula** for distance, where distance = speed × time, to find the time it takes for the cars to meet. The initial distance separating them is 150 m.
\[
\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{150 \text{ m}}{27.78 \text{ m/s}} \approx 5.4 \text{ seconds}
\]

Therefore, it will take approximately **5.4 seconds** for the two cars to meet.