Calculate the Fraction of Orange Juice in a Mixture
What are the fractions of orange juice in two 600 ml pitchers?
Data: Two 600 ml pitchers contain orange juice. One pitcher is 1/3 full and the other pitcher is 2/5 full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?
Answer:
The fraction of orange juice in the large container is 11/30.
To calculate the fraction of orange juice in the mixture in the large container, we need to determine the amount of orange juice in each of the two pitchers. The first pitcher is 1/3 full, meaning it contains 1/3 x 600 ml = 200 ml of orange juice. The second pitcher is 2/5 full, therefore it contains 2/5 x 600 ml = 240 ml of orange juice.
When both pitchers are completely filled, they each contain a total of 600 ml. Combining the two pitchers in the large container, the total volume of orange juice is 200 ml + 240 ml = 440 ml.
The total volume of the large container is 1200 ml (600 ml from each pitcher). Therefore, the fraction of orange juice in the large container is 440 ml ÷ 1200 ml = 11/30.