An extruder can fill an empty bin in 2 hours and a packaging crew can empty a full bin in 5 hours. If a bin is half full when an extruder begins to fill it and a crew begins to empty it how long will it take to fill the bin?
rate to empty bin = bin/5
rate to fill the bin = bin/2
combined rate to fill the bin = bin/2 - bin/5 = 3bin/5
time to fill half a bin = (bin/2)/(3bin/5) = 5/6 hrs. or 50 minutes.
Extruder ????
To solve this problem, we need to find the combined rate of filling and emptying the bin, and then use that rate to determine the time required to fill the bin completely. Let's break down the problem step by step:
1. Calculate the rates of filling and emptying the bin:
- The extruder can fill an empty bin in 2 hours, which means its rate of filling is 1 bin per 2 hours (1 bin/2 hours).
- The packaging crew can empty a full bin in 5 hours, which means its rate of emptying is 1 bin per 5 hours (1 bin/5 hours).
2. Determine the combined rate at which the bin is being filled and emptied:
- When the extruder starts filling the bin, it is already half full. So, the effective filling rate is cut in half.
- The combined rate is the sum of the filling rate and the emptying rate (but with the effective filling rate cut in half).
3. Calculate the time required to fill the bin:
- Divide the effective filling rate by the combined rate to find the time it takes to fill the bin.
Let's perform the calculations step by step:
1. Calculate the filling and emptying rates:
- Filling rate = 1 bin per 2 hours (1 bin/2 hours)
- Emptying rate = 1 bin per 5 hours (1 bin/5 hours)
2. Determine the combined rate:
- Combined rate = Filling rate - (Effective filling rate/2) + Emptying rate
- Effective filling rate = (1 bin/2 hours) / 2 = 1/4 bin per hour
- Combined rate = (1 bin/2 hours) - (1/4 bin per hour) + (1 bin/5 hours) = 1/10 bin per hour
3. Calculate the time to fill the bin:
- Time = 1 bin / Combined rate = (1 bin) / (1/10 bin per hour) = 10 hours
Therefore, it will take 10 hours to fill the bin completely.