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Ida worked for 135 hours to complete 3/8th of the entire job - therefore, to complete 1/8th of the entire job she took 45 hours. This means it would take her 360 hours to complete the entire job.
Since Ida can complete an eighth of the job every 5 days she finishes 2/8th of the job in the 10 days after hiring G Rene Thumb while Rene finishes the remaining 3/8th of the job in the 90 hours making her work speed at 1/8th per 30 hours.
Therefore the speed of Ida was 360 Hours to complete the job, while if Gene was originally hired she could finish the job in 240 hours - approx. 33% faster.
The exact same amount as Ida. 40 days 15(days) x 9(hours a day) = 105(hours for every 3/8) 105 ÷ 3(3/8) = 35(1/8) 35 x 8(8/8)=280 280 - 105(Amount done for 3/8) = 175(5/8) 175 ÷ 5 = 35 The same. Now to check... 15 days=3/8 30 days will equal 6/8 5 days=1/8 5x8=40
If the remainder work is 5/8, then Ida worked for 2/8 out of 5/8 of the the time because she can work 3/8 in 15 days and 1/8 in 5 days or 2/8 in 10 days. Therefore, G Rene can finish 3/8 of the garden in 10 days so at 6/8 finished garden if Rene worked on her own, it would take her 20 days and 27 days rounded up for 8/8 of the garden. Furthermore for G Rene to finish the garden on her own, it would've taken her 27 days.
By looking at the question, I notice that Ida takes 5 days to complete 1/8 of the job which means in 10 days, Ida did 2/8 of the work. In total, Ida would have done 5/8 in 25 days meaning G Rene did 3/8 in 10 days. This means that G Rene is ~33% more efficient than Ida. If G Rene was hired originally, it would take her ~26.67 days to finish compared to Ida who would take 40 days.
15 times nine is 153 hours and 20 times 9 is 180 which means that 153 is equal to 3/8 of the job and 45 hours is 1/8 of the job meaning that rene had done 4/8 of the job in ten meaning they could finish in 20 days where ida alone would take 40 days
Ida worked a total of 9X15 hours. She worked for 135 hours. 135 hours was 3/8 of the job. she was able to complete 1/8 of the job every 45 hours. Then they each worked 9 hours a day, separately for another 10 days. That means that Ida worked for 90 hours again, so she completed 2/8 more of the job. At this time, 5/8 of the job has been finished. That means that G Rene Thumb did 3/8 of the job in 90 hours. 90/3=30. Thumb took 30 hours to finish 1/8 of the job. 30x8=240. It would have taken G Rene Thumb 240 hours, or 26.6 days (rounded up to 27 days) of working 9 hours a day to finish the job by herself.
Good job people. I see some correct and some errors in these answers. I wonder if you can spot where you went wrong if you obtained different answers. The two gardeners, Ida and Rene, would finish the job in different amounts of time, with Rene being faster. Specifically, Ida would take 360 hours to finish the job while Rene would take 240 hours to finish the job.
Ida worked for 135 hours to complete 3/8th of the entire job - therefore, to complete 1/8th of the entire job she took 45 hours. This means it would take her 360 hours to complete the entire job.
ReplyDeleteSince Ida can complete an eighth of the job every 5 days she finishes 2/8th of the job in the 10 days after hiring G Rene Thumb while Rene finishes the remaining 3/8th of the job in the 90 hours making her work speed at 1/8th per 30 hours.
Therefore the speed of Ida was 360 Hours to complete the job, while if Gene was originally hired she could finish the job in 240 hours - approx. 33% faster.
Excellent job Anish. I love your added info of "33% faster". One question though, who's Gene?
DeleteThe exact same amount as Ida. 40 days
ReplyDelete15(days) x 9(hours a day) = 105(hours for every 3/8)
105 ÷ 3(3/8) = 35(1/8)
35 x 8(8/8)=280
280 - 105(Amount done for 3/8) = 175(5/8)
175 ÷ 5 = 35
The same. Now to check...
15 days=3/8
30 days will equal 6/8
5 days=1/8
5x8=40
If the remainder work is 5/8, then Ida worked for 2/8 out of 5/8 of the the time because she can work 3/8 in 15 days and 1/8 in 5 days or 2/8 in 10 days. Therefore, G Rene can finish 3/8 of the garden in 10 days so at 6/8 finished garden if Rene worked on her own, it would take her 20 days and 27 days rounded up for 8/8 of the garden. Furthermore for G Rene to finish the garden on her own, it would've taken her 27 days.
ReplyDeleteBy looking at the question, I notice that Ida takes 5 days to complete 1/8 of the job which means in 10 days, Ida did 2/8 of the work. In total, Ida would have done 5/8 in 25 days meaning G Rene did 3/8 in 10 days. This means that G Rene is ~33% more efficient than Ida. If G Rene was hired originally, it would take her ~26.67 days to finish compared to Ida who would take 40 days.
ReplyDelete15 times nine is 153 hours and 20 times 9 is 180 which means that 153 is equal to 3/8 of the job and 45 hours is 1/8 of the job meaning that rene had done 4/8 of the job in ten meaning they could finish in 20 days where ida alone would take 40 days
ReplyDeleteIda worked a total of 9X15 hours. She worked for 135 hours. 135 hours was 3/8 of the job. she was able to complete 1/8 of the job every 45 hours. Then they each worked 9 hours a day, separately for another 10 days. That means that Ida worked for 90 hours again, so she completed 2/8 more of the job. At this time, 5/8 of the job has been finished. That means that G Rene Thumb did 3/8 of the job in 90 hours. 90/3=30. Thumb took 30 hours to finish 1/8 of the job. 30x8=240. It would have taken G Rene Thumb 240 hours, or 26.6 days (rounded up to 27 days) of working 9 hours a day to finish the job by herself.
ReplyDeleteGood job people. I see some correct and some errors in these answers. I wonder if you can spot where you went wrong if you obtained different answers. The two gardeners, Ida and Rene, would finish the job in different amounts of time, with Rene being faster. Specifically, Ida would take 360 hours to finish the job while Rene would take 240 hours to finish the job.
ReplyDelete