A car and a motorcycle leave the city at the same time to drive to a lake 120 km away. The motorcycle's speed is 20 km/h greater than the car's speed, and it arrives at the lake 1 hour earlier than the car. What are the speeds of the car and the motorcycle?

Mathematics Questions

A car and a motorcycle leave the city at the same time to drive to a lake 120 km away. The motorcycle’s speed is 20 km/h greater than the car’s speed, and it arrives at the lake 1 hour earlier than the car. What are the speeds of the car and the motorcycle?

Short Answer

The speed of the car is determined to be 40 km/h, while the motorcycle travels at 60 km/h, as it is 20 km/h faster than the car. This conclusion is reached by setting up an equation based on the time taken by both vehicles to cover a distance of 120 km.

Step-by-Step Solution

Step 1: Define Variables

Let the speed of the car be represented as x. Consequently, the speed of the motorcycle will be (x + 20), since it travels 20 km/h faster than the car. Both vehicles are covering a distance of 120 km.

Step 2: Set Up the Equation

We can relate the distance, speed, and time using the formula for time. The time taken by the car can be expressed as (120/x) and the time taken by the motorcycle as (120/(x + 20)). According to the problem, the motorcycle takes 1 hour less than the car, establishing the following equation:

120/x = 120/(x + 20) + 1

Step 3: Solve for Speed

Cross-multiplication leads to a quadratic equation: x¬¨‚â§ + 20x – 2400 = 0. Factoring or using the quadratic formula yields x = 40. Therefore, the speed of the car is 40 km/h, and subsequently, the speed of the motorcycle is 60 km/h.

A car and a motorcycle leave the city at the …