The fraction 4/3 is equivalent to A: 3/4 B: 5/4 C: 1 1/3 D: 4 1/3
1 answer:
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Answer:
See the attached figure.
Step-by-step explanation:
Modeling each part as a function.
Let x is hours of the working day
The company packs 80 boxes of toys every hour for the first 3 hours of the day. ⇒ y₁ = 80 x , x ∈ [0,3]
At the end of the 3 hours The company packs = 80 * 3 = 240
They stop packaging for the next 2 hours in order to carry out a training session. ⇒ y₂ = 240 , x ∈ [3,5]
Then, for the next 4 hours, they pack 20 boxes of toys every hour
y₃ = 20x + c , x ∈ [5,9]
To find c, y₂ = y₃ at x =5
∴ 240 = 20 * 5 + c
∴ c = 240 - 20 * 5 =240 - 100 = 140
∴ y₃ = 20x + 140 , x ∈ [5,9]
So,
y₁ = 80 x , x ∈ [0,3]
y₂ = 240 , x ∈ [3,5]
y₃ = 20x + 140 , x ∈ [5,9]
The graph models the piecewise function for the given situation is as shown in the attached figure.
Answer:
Levi's dad takes 1.67 hours to wash the car by himself
Step-by-step explanation:
* Lets explain how to solve the problem
- Levi takes 2.5 hours to wash his dad's car alone
- Levi and his dad take 1 hour to wash the dad's car together
∵ Levi takes 2.5 hours to wash the car alone
∴ The rate of Levi is 1/2.5 car/hr
∵ His dad takes x hours to wash the car alone
∴ The rate of his dad is 1/x car/hr
∵ They working together for 1 hour to wash the car
- The equation of the work is rate of Levi × t + rate of his dad × t = 1
∵ t is the time of working together
∵ t = 1 hour
∴
- Multiply both sides by 2.5x to cancel the denominators
∵
∵ 1 × (2.5x) = 2.5x
∴ x + 2.5 = 2.5x
- Subtract x from both sides
∴ 2.5 = 1.5x
- Divide both sides by 1.5
∴ x = 5/3 ≅ 1.67
∵ x is the the time of his dad to wash the car alone
∴ Levi's dad takes 1.67 hours to wash the car by himself