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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