SOLUTION: Mark and Luke can paint a room together in 4 hours if it takes mark 9 hours to paint by himself how long will it take luke to paint by himself?
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Question 1156528: Mark and Luke can paint a room together in 4 hours if it takes mark 9 hours to paint by himself how long will it take luke to paint by himself? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52855) (Show Source):
Working together, they make of the job per hour.
Working alone, Mark makes of the job per hour.
Hence, Luke makes - = - = of the job per hour.
It means that Luke will complete the job in = hours = 7 hours and 12 minutes. ANSWER
Here are a couple of alternatives to the standard solution method shown by tutor @ikleyn.
Try using all three methods and find the one that works best for you....
(1) Together they take 4 hours to do the job; Mark alone takes 9 hours. So in the 4 hours that they work together, Mark does 4/9 of the job.
That means Luke in those 4 hours does 5/9 of the job.
So the amount of time it takes Luke to do the job alone is 4*(9/5) = 36/5 = 7.2 hours.
As an alternative for the last step by this method, note that Luke works 5/4 as fast as Mark, so the amount of time it takes him alone is 4/5 of the time it takes Mark alone: 9*(4/5) = 36/5.
(2) Consider the least common multiple of the two given times, which is 36 hours.
In 36 hours, Mark could do the job 36/4 = 9 times, and together they could do it 36/9 = 4 times.
That means in 36 hours Luke could do the job 9-4 = 5 times.
So the amount of time Luke would take to do the job alone is 36/5 = 7.2 hours.
