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James can complete a job in 6 hours and Sarah can complete the same jo
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08 Feb 2019, 13:44
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56% (03:00) correct 44% (03:31) wrong based on 41 sessions
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James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone? A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes
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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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08 Feb 2019, 19:51
SajjadAhmad wrote: James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?
A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes Let J work for 2x hours alone, so S works alone for x hours.. Both combined, can do 2/9+1/6=7/18 or work in 1 hour... So 2x/6+2x/9+7/18=1.....(6x+4x)/18=11/18....x=1.1=1hr 6 minutes.. James works alone for 2x, so 2hrs 12 min C
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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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09 Feb 2019, 01:10
SajjadAhmad wrote: James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?
A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes Since James can complete the job in 6 hours and Sarah in 4.5 hours, lets total work be 54 units. We choose 54 as it is a number that is compatible with both the times.The rates at which James and Sarah do the work is 9 units and 12 units respectively. In 1 hour, they will both complete 21(9 + 12) units of work. Let the time on which James does the work alone be x hours. James will do is 9x units or work and Sarah does \(12(\frac{x}{2})\) or \(6x\) units. \(9x + 6x + 21 = 54\) > \(15x = 54  21 = 33\) > \(x = \frac{33}{15} = 2\frac{1}{5}\) hours Therefore, the total time that James works on the job alone is 2 hours, 12 minutes(Option C)
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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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09 Feb 2019, 01:12
SajjadAhmad wrote: James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?
A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes rate of James= 1/6 and rate of Sarah = 2/9 let time of James = 2hrs and Sarah = 1 hour work done by both James & Sarah ; 1/6+2/9 = 7/18 in 1 hr so total work done 2x/6+2x/9+7/18 = 1 x= 1.1 hrs or 1 hr 6 mins James work is for 2 hours so 2*1.1 = 2 hrs 12 mins IMO C
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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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09 Feb 2019, 01:21
SajjadAhmad wrote: James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?
A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes Lets take work as 36 units James rate = 36/6 = 6 units/hr Sarah rate = 8 units / hr 1 hour for them to complete the remainder of the job together, means remaining work = 3614 = 22 units W = rate *time let time taken by James to complete the work be x If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James 6x + 4x = 22 x = 22/10 = 11/5 how long did James work on the job alone = 2 hours, 12 minutes
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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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15 Mar 2019, 13:25
Making a rates table:
1) Set work to be LCM of 6 and 4.5... 18 2) Find rate of James and Sarah
______r__t______W James 3 * 6 hr = 18 Sarah 4 * 4.5 hr = 18
Next part: ______r__t_____W James 3 * t hr = Sarah 4 * 0.5t hr = Ja+Sa 7 * 1 hr = 7
From this we can make the equation 3t+2t = 11 (James' work + Sarah's work = 11 remaining out of 18) So, t = 11/5 OR 2 and 1/5 hours... 1/5 of an hour is 12 minutes so the answer is C. Or just set up the ratio 11 hrs/5 * 60 min/1 hr = 132 minutes or 2 hours 12 minutes.



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Re: James can complete a job in 6 hours and Sarah can complete the same jo
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15 Jul 2019, 07:32
SajjadAhmad wrote: James can complete a job in 6 hours and Sarah can complete the same job in 4 \(\frac{1}{2}\) hours. If James works on the job alone for a certain amount of time and Sarah works on the job alone for half as long as James, and it takes 1 hour for them to complete the remainder of the job together, how long did James work on the job alone?
A. 1 hour, 6 minutes B. 1 hour, 10 minutes C. 2 hours, 12 minutes D. 2 hours, 20 minutes E. 3 hours, 18 minutes James does = 1/6 units in 1 hour Sarah does = 9/2 units in 1 hour Together they do = 1/6 + 2/9 = 7/18 units in 1 hour Before this 1 hour of working together , they were working alone... They did the rest = 1  7/18 = 11/18 units working alone... Lets say , James worked for x hours during that time ... And Sarah worked for x/2 hours... So x/6 + x/9 = 11/18 x= 11/5 hours... C is the answer... Please give me Kudos if you liked my explanation.




Re: James can complete a job in 6 hours and Sarah can complete the same jo
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