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03 Dec 2021, 02:12
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Charlie can eat a large box of doughnuts in 4 hours. If Charlie and Milena eat simultaneously at their respective, constant rates, they can finish a large box of doughnuts in 2.5 hours. How many hours would it take Milena to eat the box of doughnuts by herself?
A. \(\frac{3}{20}\)
B. \(\frac{3}{2}\)
C. \(\frac{20}{13}\)
D. \(\frac{13}{2}\)
E. \(\frac{20}{3}\)
A. \(\frac{3}{20}\)
B. \(\frac{3}{2}\)
C. \(\frac{20}{13}\)
D. \(\frac{13}{2}\)
E. \(\frac{20}{3}\)
03 Dec 2021, 02:12
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Official Solution:
Charlie can eat a large box of doughnuts in 4 hours. If Charlie and Milena eat simultaneously at their respective, constant rates, they can finish a large box of doughnuts in 2.5 hours. How many hours would it take Milena to eat the box of doughnuts by herself?
A. \(\frac{3}{20}\)
B. \(\frac{3}{2}\)
C. \(\frac{20}{13}\)
D. \(\frac{13}{2}\)
E. \(\frac{20}{3}\)
Say it would take Milena \(x\) hours to eat the box of doughnuts by herself. Then in 1 hour she can eat \(\frac{1}{x}\) part of the box.
In 1 hour Charlie can eat \(\frac{1}{4}\) part of the box.
In 1 hour Charlie and Milena together can eat \(\frac{1}{x} + \frac{1}{4}\) part of the box.
We are given that \(\frac{1}{x} + \frac{1}{4}=\frac{1}{2.5}\).
\(\frac{1}{x} = \frac{2}{5}-\frac{1}{4}\)
\(\frac{1}{x} = \frac{3}{20}\)
\(x=\frac{20}{3}\) hours.
Answer: E
Charlie can eat a large box of doughnuts in 4 hours. If Charlie and Milena eat simultaneously at their respective, constant rates, they can finish a large box of doughnuts in 2.5 hours. How many hours would it take Milena to eat the box of doughnuts by herself?
A. \(\frac{3}{20}\)
B. \(\frac{3}{2}\)
C. \(\frac{20}{13}\)
D. \(\frac{13}{2}\)
E. \(\frac{20}{3}\)
Say it would take Milena \(x\) hours to eat the box of doughnuts by herself. Then in 1 hour she can eat \(\frac{1}{x}\) part of the box.
In 1 hour Charlie can eat \(\frac{1}{4}\) part of the box.
In 1 hour Charlie and Milena together can eat \(\frac{1}{x} + \frac{1}{4}\) part of the box.
We are given that \(\frac{1}{x} + \frac{1}{4}=\frac{1}{2.5}\).
\(\frac{1}{x} = \frac{2}{5}-\frac{1}{4}\)
\(\frac{1}{x} = \frac{3}{20}\)
\(x=\frac{20}{3}\) hours.
Answer: E
