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There are 8 fields of exactly the same size that are to be p
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15 Oct 2018, 14:13
15 Oct 2018, 14:13
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Question Stats:
75% (01:51) correct
25% (02:00) wrong based on 36 sessions
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There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?
Show: :: HOURS
20
Re: There are 8 fields of exactly the same size that are to be p
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15 Oct 2018, 20:07
15 Oct 2018, 20:07
1
Carcass wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?
Show: :: HOURS
20
Amount of work = Rate * time
Now for the first case
"5 hours for 4 of the farmers to plow the first 2 fields"
it can be written as:
\(2 = 4 * Rate * 5\)
or Rate = \(\frac{2}{20} = \frac{1}{10}\)
Now, time taken for 3 farmers to plow the remaining 6 fields
Amount of work = Rate * time
\(6 = 3 * \frac{1}{10} * Time\)
or Time = 20 hours
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Re: There are 8 fields of exactly the same size that are to be p
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16 Oct 2018, 07:35
16 Oct 2018, 07:35
1
Carcass wrote:
There are 8 fields of exactly the same size that are to be plowed by 7 farmers who work at identical rates. If it takes 5 hours for 4 of the farmers to plow the first 2 fields, how many hours will it take the remaining 3 farmers to plow the remaining 6 fields?
Show: :: HOURS
20
We can use some logic to reach the correct answer.
GIVEN: It takes 5 hours for 4 farmers to plow 2 fields
So, it takes 2.5 hours for 4 farmers to plow 1 field [it takes 1/2 the time to plow 1/2 as many fields]
So, it takes 10 hours for 1 farmer to plow 1 field [if we have ONE-FOURTH as many workers, then it takes 4 TIMES as long to complete the job]
So, it takes 60 hours for 1 farmer to plow 6 fields [if the 1 farmer works 6 TIMES as long, he/she can plow 6 TIMES as many fields]
So, it takes 20 hours for 3 farmers to plow 6 fields [if we TRIPLE the number of workers, the work time is ONE-THIRD as long]
Answer: 20
Cheers,
Brent
