A carload of stone taken from a quarry by the plug-and-feather method contains pieces of stone have a mean weight of 1,500 pounds and a total weight of 36,000 pounds. Another carload of stone produced by the explosive method (where stone is blasted into random shapes by explosives) contains pieces of stone that have a mean weight of 600 pounds and a total weight of 30,000 pounds. What is the mean weight of all the pieces of stone combined?
To find the mean weight of all the pieces of stone combined, we need to calculate the total weight of all the pieces and then divide it by the total number of pieces.
First, let's establish the number of pieces for each carload. We can do this by dividing the total weight of each carload by the mean weight of the pieces.
For the plug-and-feather carload:
Number of pieces = Total weight / Mean weight = 36,000 pounds / 1,500 pounds = 24 pieces
For the explosive carload:
Number of pieces = Total weight / Mean weight = 30,000 pounds / 600 pounds = 50 pieces
Next, let's calculate the total weight of all the pieces by adding the weights of the pieces from each carload.
Total weight of all pieces = Total weight of plug-and-feather carload + Total weight of explosive carload
Total weight of all pieces = 36,000 pounds + 30,000 pounds = 66,000 pounds
Now, we can find the mean weight of all the pieces combined by dividing the total weight of all the pieces by the total number of pieces.
Mean weight of all pieces combined = Total weight of all pieces / Total number of pieces
Mean weight of all pieces combined = 66,000 pounds / (24 pieces + 50 pieces)
Mean weight of all pieces combined = 66,000 pounds / 74 pieces
Calculating this division, we find that the mean weight of all the pieces of stone combined is approximately 891.89 pounds.