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02 Sep 2020, 22:00
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Difficulty:
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83% (01:13) correct
17%
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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) 3/20
(B) 3/2
(C) 20/13
(D) 13/2
(E) 20/3
M37-83
(A) 3/20
(B) 3/2
(C) 20/13
(D) 13/2
(E) 20/3
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M37-83
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03 Dec 2021, 02:13
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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
General Discussion
02 Sep 2020, 22:23
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Charlie – in 4 hours
Charlie and Milena – in 2.5 hours
Milena – in x hours
An easy way: if Ch and M had a similar rate, 4 hours each, then they would finish in 2 hours. Since it takes more than 2 hours, namely 2.5 hours, then M must eat slower than Ch. So, x must be greater than 4. Hence, A, B, and C are out. We can risk to choose between D and E. 50% chance.
Algebraic solution:
Charlie eats 1/4 of box in an hour
Milana eats 1/x of box in an hour
Together they must finish 1/1 of box in 2.5 hours.
So, (1/4 + 1/x)*2.5 = 1 ; x = 20/3
Milena takes 20/3 hours to finish herself.
Hence E
Posted from my mobile device
Charlie and Milena – in 2.5 hours
Milena – in x hours
An easy way: if Ch and M had a similar rate, 4 hours each, then they would finish in 2 hours. Since it takes more than 2 hours, namely 2.5 hours, then M must eat slower than Ch. So, x must be greater than 4. Hence, A, B, and C are out. We can risk to choose between D and E. 50% chance.
Algebraic solution:
Charlie eats 1/4 of box in an hour
Milana eats 1/x of box in an hour
Together they must finish 1/1 of box in 2.5 hours.
So, (1/4 + 1/x)*2.5 = 1 ; x = 20/3
Milena takes 20/3 hours to finish herself.
Hence E
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