Car B is twice as fast as car A. If car A covers 90 km in 2 hours, what is the speed of car B? A. 90 kmph B. 80 kmph C. 100 kmph D. 70 kmph
A
Understanding the Car Speed Problem
This question asks us to determine the speed of car B, given information about car A's speed and the relationship between the speeds of car A and car B. We are told how far car A travels and in what time, which allows us to calculate car A's speed. We are also told that car B is twice as fast as car A.
Calculating the Speed of Car A
The speed of an object is calculated by dividing the distance covered by the time taken. The formula is:
Speed = \(\frac{\text{Distance}}{\text{Time}}\)
We are given that car A covers 90 km in 2 hours.
Using the formula:
Speed of Car A = \(\frac{90\text{ km}}{2\text{ hours}}\)
Let's perform the calculation:
Speed of Car A = \(45\text{ km/h}\)
So, the speed of car A is 45 kmph.
Calculating the Speed of Car B
The question states that car B is twice as fast as car A. This means the speed of car B is two times the speed of car A.
Speed of Car B = 2 × Speed of Car A
We found the Speed of Car A to be 45 kmph. Now, we can calculate the speed of car B:
Speed of Car B = 2 × 45 km/h
Let's perform the multiplication:
Speed of Car B = 90 km/h
Therefore, the speed of car B is 90 kmph.
Conclusion on Car Speeds
Based on the calculations, the speed of car B is 90 kmph.
| Vehicle | Distance | Time | Calculated Speed |
|---|---|---|---|
| Car A | 90 km | 2 hours | \(\frac{90}{2} = 45\) km/h |
| Car B | N/A (Related to Car A) | N/A | \(2 \times \text{Speed of A} = 2 \times 45 = 90\) km/h |
Revision Table: Speed, Distance, Time Concepts
| Concept | Formula | Units (Common) |
|---|---|---|
| Speed | \(\frac{\text{Distance}}{\text{Time}}\) | km/h, m/s, miles/hour |
| Distance | Speed × Time | km, meters, miles |
| Time | \(\frac{\text{Distance}}{\text{Speed}}\) | hours, seconds, minutes |
Additional Information on Speed Calculations
Understanding the relationship between speed, distance, and time is fundamental in solving problems like this. Speed measures how quickly an object moves over a certain distance. Distance is the total length traveled, and time is the duration of the travel.
- Always ensure that the units for distance and time are consistent when calculating speed. For example, if distance is in kilometers, time should be in hours to get speed in km/h.
- Relative speed concepts are used when dealing with multiple moving objects, but in this problem, we only need the absolute speed of each car individually.
- Word problems often provide information in a narrative format that needs to be translated into mathematical equations to solve. Identifying the knowns (distance, time, relationships) and the unknown (speed of car B) is the first step.
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