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Otto takes 20 days to empty a 50 liter barrel of beer and

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CEO
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Otto takes 20 days to empty a 50 liter barrel of beer and [#permalink] New post 19 Oct 2007, 12:34
Otto takes 20 days to empty a 50 liter barrel of beer and together with Hanna he can empty it in 14 days, how many days will it take Hanna to finish a barrel by herself?

17
33
39
47
58

Please explain your logic.
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Re: Challenge - Beer [#permalink] New post 19 Oct 2007, 13:30
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bmwhype2 wrote:
Otto takes 20 days to empty a 50 liter barrel of beer and together with Hanna he can empty it in 14 days, how many days will it take Hanna to finish a barrel by herself?

17
33
39
47
58

Please explain your logic.


speed of Otto = 50/20
speed of Hanna= 50/x

50/20+50/x=50/14------------>x=47
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Re: Challenge - Beer [#permalink] New post 19 Oct 2007, 13:30
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bmwhype2 wrote:
Otto takes 20 days to empty a 50 liter barrel of beer and together with Hanna he can empty it in 14 days, how many days will it take Hanna to finish a barrel by herself?

17
33
39
47
58

Please explain your logic.


rates:
Otto can drink 50/20 litres per day
Hannah can drink 50/x litres per day
together they can drink 50/14 per day

50/20+50/x=50/14

1/20+1/x=1/14

x+20=20x/14
14x+280=20x
6x=280
x=46.666..

x~47
CEO
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Re: Challenge - Beer [#permalink] New post 29 Jan 2008, 10:08
1/20 + 1/H = 1/14

1/H = 1/20 - 1/14
1/H = 10/140 - 7/140
1/H = 3/140

time = 140/3
approx 47

OA is D
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Re: Challenge - Beer [#permalink] New post 29 Jan 2008, 13:21
bmwhype2 wrote:
Otto takes 20 days to empty a 50 liter barrel of beer and together with Hanna he can empty it in 14 days, how many days will it take Hanna to finish a barrel by herself?

17
33
39
47
58

Please explain your logic.


50/20 + 50/X = 50/14
1/X = 3/140
X ~ 47

The answer is (D)
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Re: Challenge - Beer [#permalink] New post 29 Jan 2008, 19:34
ottos rate is 2.5 litres per day (50/20). let hannahs rate be x.

together, we can express as such: (2.5+x)*14 = 50 -->x=15/14 litres per day for hannah

this leads to approx 47 days to finish 50 litres
Re: Challenge - Beer   [#permalink] 29 Jan 2008, 19:34
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Otto takes 20 days to empty a 50 liter barrel of beer and

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