A juice bottling plant has purchased a new electric bottling machine.

Question

A juice bottling plant has purchased a new electric bottling machine. Working at a constant rate, the machine bottles R liters of juice per hour. As the machine works, it bottles C liters of juice per dollar spent on its operating and maintenance costs.

In terms of R and C, determine how many hours it will take to spend $20 on the machine's operating and maintenance costs. Then determine how many dollars will be spent in 3 minutes. Make one choice in each column.

Joseph67890 · Answer

Rate * time = Work

1. Rate = "R" , Time = ? , work = 20*C
 Time = 20C/R

2. Time = 3 min but rate R is in hours , therefore converting mins to hours = 3/60 = 1/20
Rate = "R" , Time = 1/20 , work = amount*C
 Amount = R/20C

Apt0810 · Answer

A)1$-> C litre
20$ -> 20C litre
R litre -> 1 hour
20C-> 20C/R

B) 60minutes =R litre
3 minutes= R/20
1$->C litre
R/20C $ spent

Posted from my mobile device

napolean92728 · Answer

Definitions:
 
  R  = liters per hour bottled 
  C  = liters per dollar spent
 → So,  C liters = $1 
 → Or  1 liter = $1/C

Part 1: How many hours it will take to spend $20 
We are given:
 
 Machine bottles  R liters/hour  
 It costs  $1 for every C liters , so:
 
  Cost per hour  = (R liters/hour) × (1 dollar / C liters) =  R/C dollars per hour   
  
To find  time (in hours) to spend $20 , we use:
 	ext{Time} = \frac{	ext{Total Cost}}{	ext{Cost per Hour}} = \frac{20}{R/C} = \frac{20C}{R} 
✔️ Correct value for hours to spend $20:  20C/R

Part 2: How many dollars will be spent in 3 minutes 
3 minutes =  3/60 = 1/20 hours 
We already found that  Cost per hour = R/C dollars 
Cost in 1/20 hour= 	ext{Cost in 1/20 hour} = \left(\frac{R}{C}ight) 	imes \left(\frac{1}{20}ight) = \frac{R}{20C} 
✔️ Correct value for dollars spent in 3 minutes:  R/20C

Final Answers:
 
  Hours to Spend $20 :  20C/R  
  Dollars Spent in 3 Minutes :  R/20C

Hours to Spend $20	Dollars Spent in 3 Minutes	Values
		20/RC
		20R/C
		20C/R
		R/20C
		RC/20
		C/20R

A juice bottling plant has purchased a new electric bottling machine.

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A juice bottling plant has purchased a new electric bottling machine.

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