After loading a dock, each worker on the night crew loaded 3/4 as many boxes…
2024
After loading a dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day of the crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by two crews did the day crew load?
- A.
1 by 2
- B.
2 by 5
- C.
4 by 5
- D.
5 by 8
Attempted by 791 students.
Show answer & explanation
Correct answer: D
Answer: 5/8
Algebraic derivation:
Let each day worker load x boxes and let there be w day workers. Then day crew total = x·w.
Each night worker loads (3/4)x, and there are (4/5)w night workers, so night crew total = (3/4 x)·(4/5 w) = (3/5)x·w.
Fraction loaded by the day crew = xw / (xw + (3/5)xw) = 1 / (1 + 3/5) = 1 / (8/5) = 5/8.
Numeric check:
Take x = 4 boxes per day worker and w = 5 day workers. Day total = 4·5 = 20.
Night per worker = 3, night workers = 4, night total = 3·4 = 12. Day fraction = 20/(20+12) = 20/32 = 5/8, which matches the algebraic result.