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: Determine the total relative distance the car gained on the bus. Initially, the car was 90 km behind. Finally, it is 90 km ahead. The total distance the car needed to gain is the initial gap plus the final lead. Relative Distance = \( 90 \, \text{km} + 90 \, \text{km} = 180 \, \text{km} \).

Step 2: Calculate the relative speed of the car with respect to the bus. Relative Speed = \( \frac{\text{Relative Distance}}{\text{Time}} \). Relative Speed = \( \frac{180 \, \text{km}}{3 \, \text{h}} = 60 \, \text{km/h} \).

Step 3: Calculate the actual speed of the car. When two objects move in the same direction, their relative speed is the difference between their individual speeds. Relative Speed = Speed of Car - Speed of Bus. \( 60 = \text{Speed of Car} - 45 \). Speed of Car = \( 60 + 45 = 105 \, \text{km/h} \).