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If bob and bill work together, they can do a job in 3h 44 min. If it takes Bob one hour more to the job than it takes Bill,
find the time it would take each of them working alone to do the job.
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3 hours 44 minutes = 224 minutes.
Let x be the number of minutes (amount of time, in minutes) for Bill to complete the job working alone.
Then the number of minutes (amount of time, in minutes) for Bob to complete the job working alone is x + 60, according to the condition.
Working alone, Bill complete of the job in one minute (in each minute). It is Bill's rate of work.
Working alone, Bob complete of the job in one minute (in each minute). It is Bob's rate of work.
Working together, Bob and Bill make of the job per minute.
In other words, their combined rate of work is the sum of their individual rates.
From the other side, we know from the condition, that Bob and Bill make of the job per minute working together.
So, we have this equation to determine x
= .
To solve it, multiply both sides by 224*x*(x+60) to rid of denominators. You will get
224(x+60) + 224x = x*(x+60), or
448x + 13440 = , or
= ,
= = .
Only positive root is acceptable. It is x = 420 minutes, or x = 7 hours.
Answer. Bill can complete the job in 7 hours working alone.
Bob can do it in 8 hours working alone.