A car takes 3 hours to travel a distance of 240 km with a speed of 80 km/h while a motorbike can cover the same distance in 4 hours if its travels at a speed of 60 km/h. Explain why the speed and the time it takes for the vehicles to travel a certain distance exhibit an inverse variation.
this is because as the speed of a vehicle is high or low then the time required to cover a certain distance will be less or more respectively
To understand why the speed and the time it takes for the vehicles to travel a certain distance exhibit an inverse variation, we need to analyze the relationship between speed, time, and distance.
Let's consider the car first. We know that the car travels a distance of 240 km in 3 hours and has a speed of 80 km/h. We can use the formula: speed = distance / time to verify this.
Speed = 240 km / 3 hours = 80 km/h
Now, let's analyze the motorbike. It covers the same distance of 240 km in 4 hours while traveling at a speed of 60 km/h.
Speed = 240 km / 4 hours = 60 km/h
By analyzing the data from both the car and the motorbike, we observe the following:
- In the case of the car, if the speed increases, the time it takes to cover the distance decreases. For example, if the car were to travel at 160 km/h, it would cover the distance in half the time, i.e., 1.5 hours.
- In the case of the motorbike, if the speed decreases, the time it takes to cover the distance increases. For instance, if the motorbike were to travel at 30 km/h, it would take 8 hours to cover the distance.
Based on this analysis, we can conclude that the speed and the time it takes to travel a certain distance exhibit an inverse variation. Inverse variation means that as one quantity increases, the other decreases, and vice versa.
In simple terms, if you increase the speed at which you travel, you will cover the distance in less time. Conversely, if you decrease the speed at which you travel, it will take more time to cover the same distance.