Time in hours Speed in kph 1 4/5 2/3 4/7 1/2 40 50 60 70 80 1. How do the speed and time of travel affect each other? 2. Write a mathematical statement to represent the relation. 3. Is there a constant number involved? Explain the process that you have used in finding out.
Answer (2)
To find a constant, we'd need to know the distance traveled in each case. If the distance is the same for all scenarios, then the product of speed and time would be constant.Example: Let's assume the distance traveled in each scenario is 100 kilometers. - Scenario 1: Speed = 40 kph, Time = 2.5 hours. Distance = 40 * 2.5 = 100 km. - Scenario 2: Speed = 50 kph, Time = 2 hours. Distance = 50 * 2 = 100 km. - Scenario 3: Speed = 60 kph, Time = 1.67 hours (approximately). Distance = 60 * 1.67 = 100 km (approximately).In this example, the product of speed and time (which represents distance) is constant, even though the individual values of speed and time vary. Process Used:Understanding the Concept: We started by understanding the inverse relationship between speed and time.Formula: We applied the formula "Distance = Speed x Time".Example: We created an example scenario with a constant distance to illustrate how the product of speed and time remains constant when distance is fixed.
Answer:Here’s a structured approach to your questions about the relationship between speed, time, and travel:Given DataTime (in hours): 95,23,47,1259 , 32 , 74 , 21 Speed (in kph): 40,50,60,70,8040,50,60,70,801. How do the speed and time of travel affect each other?The speed and time of travel are inversely related when distance is constant. This means:If the speed increases, the time taken to travel a certain distance decreases.Conversely, if the speed decreases, the time taken increases.This relationship can be explained through the formula for distance, which states that:Distance=Speed×TimeDistance=Speed×Time2. Write a mathematical statement to represent the relation.From the distance formula, we can express the relationship mathematically as:=×D=S×TWhere:D = DistanceS = SpeedT = TimeIf we are considering a constant distance, we can rearrange this to express time in terms of speed:=T= SD This shows that for a constant distance D, time T varies inversely with speed S.3. Is there a constant number involved? Explain the process that you have used in finding out.Yes, the constant number involved in this relationship is the distance D.Explanation of the Process:To find the relationship, we start from the basic distance formula.We recognize that if distance remains constant, then speed and time must vary in such a way that their product remains equal to that constant distance.As speed changes, we can calculate the corresponding time by dividing the constant distance by the speed.For example, if we assume the distance =100D=100 km, we can find the time for different speeds:For =40S=40 kph:=100 km40 kph=2.5 hoursT= 40 kph100 km =2.5 hoursFor =50S=50 kph:=100 km50 kph=2 hoursT= 50 kph100 km =2 hoursThis process continues for each speed, demonstrating how time decreases as speed increases for the same distance.If you have any more questions or need further clarification, feel free to ask!
