Respuesta :
Concept #1: Speed Formulae
We know the formulae:
[tex]\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]
Let us solve an example to understand the concept better.
Example:
Question: Find the speed of a car which travelled 12 km in 2 hours.
Solution: We know the following
- Car travelled (Distance): 12 km
- Time travelled: 2 hours
Substitute the information provided into the speed formula:
[tex]\implies \text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]
[tex]\implies \text{Speed} = \dfrac{\text{12 km}}{\text{2 hours}} = \boxed{6 \ \text{km/hour}}[/tex]
Therefore, the speed of the car is 6 kilometers per hour.
Concept #2: Distance Formulae
From the previous concept, we had:
[tex]\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}[/tex]
Finding the distance formula through step-by step work:
Let Speed = S, Distance = D, and Time = T.
[tex]\implies \text{S} = \dfrac{\text{D}}{\text{T}}[/tex]
Multiply "t" on both sides:
[tex]\implies \text{S} \times \text{T}= \dfrac{\text{D}}{\text{T}} \times \text{T}[/tex]
[tex]\implies \text{S} \times \text{T}={\text{D}[/tex]
From the above work, we can say that Distance = Speed × Time.
Let us solve an example to understand the concept better.
Example:
Question: A train travelled from point A at a speed of 16 km/h in 2 hours to reach point B. Find the distance (Point A - Point B) travelled by the train.
Solution: We know the following
- Speed of train: 16 km/h
- Time taken to travel from A to B: 2 hours
Substitute the information provided into the distance formula:
[tex]\implies \text{Distance = Speed} \times \text{Time}[/tex]
[tex]\implies \text{Distance = 16 km/h} \times \text{2 hours}[/tex]
⇒ Distance = 16 km × 2 = 32 km
Therefore, the train travelled 32 km to reach point B.
Concept #3: Time Formulae
From the previous concept, we had:
[tex]\text{Distance = Speed} \times \text{Time}[/tex]
Finding the time formula through step-by step work:
Let distance = D, speed = S, and time = T
[tex]\implies \text{D = S} \times \text{T}[/tex]
Dividing "S" both sides:
[tex]\implies \dfrac{\text{D}}{\text{S}} = \dfrac{\text{S} \times \text{T}}{\text{S}}[/tex]
[tex]\implies \dfrac{\text{D}}{\text{S}} = \text{T}[/tex]
From the above work, we can say that Distance/Speed = Time.
Let us solve an example to understand the concept better.
Example:
Question: A plane traveled 200 km at a speed of 100 km/h. How much time did it take to travel 200 km?
Solution: We know the following
- Distance travelled by the plane: 200 km
- Speed of plane: 100 km/h
Substitute the information provided into the time formula:
[tex]\implies \text{Time} = \dfrac{\text{Distance}}{\text{Speed}}[/tex]
[tex]\implies \text{Time} = \dfrac{\text{200 km}}{\text{100 km/h}} = \dfrac{\text{2 km}}{\text{1 km/h}} = \boxed{\text{2 hours}}[/tex]
Therefore, it took 2 hours to travel 200 km at a speed of 100 km/h.
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