Question

On a straight road, a bus is 90 km ahead of a car running in the same direction. After 3 hours, the car is 90 km ahead of the bus. If the speed of the bus is 45 km/h, then what is the speed of the car (in km/h)?

• A. 90
• B. 92
• C. 95
• D. 105

Hint:

Relative speed is the key concept when dealing with moving objects. For same-direction travel, it's the difference; for opposite-direction travel, it's the sum.

Answer 1

The Correct Option is D

Step 1: Calculate the total relative distance the car gained on the bus. The car initially trailed by 90 km and ended 90 km ahead. Therefore, the total distance gained equals the initial gap plus the final lead. Relative Distance = \( 90 \, \text{km} + 90 \, \text{km} = 180 \, \text{km} \).

Step 2: Determine the relative speed of the car compared to the bus. Relative Speed is calculated as: \( \frac{\text{Relative Distance}}{\text{Time}} \).Relative Speed = \( \frac{180 \, \text{km}}{3 \, \text{h}} = 60 \, \text{km/h} \).

Step 3: Find the car's actual speed. With objects moving in the same direction, relative speed is the difference in individual speeds.Relative Speed = Speed of Car - Speed of Bus.\( 60 = \text{Speed of Car} - 45 \).Speed of Car = \( 60 + 45 = 105 \, \text{km/h} \).