SOLUTION: Mary and Jane could finish a job in 1 hour. After Mary worked in the job for 2 hours, Jane joined her and together they finished the job in 20 minutes. How long will each of them f

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Question 582314: Mary and Jane could finish a job in 1 hour. After Mary worked in the job for 2 hours, Jane joined her and together they finished the job in 20 minutes. How long will each of them finish the job working alone?
*please answer the problem with 2 equations and 2 unknowns(x and y). thanks!
Answer by Edwin McCravy(20054) (Show Source):
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Mary and Jane could finish a job in 1 hour. After Mary worked in the job for 2 hours, Jane joined her and together they finished the job in 20 minutes. How long will each of them finish the job working alone?
*please answer the problem with 2 equations and 2 unknowns(x and y). thanks!

Let x = the number of hours it would take Mary to finish 1 job working alone. Let y = the number of hours it would take Jane to finish 1 job working alone. 20 minutes = 1/3 hour Make this chart: No. of jobs No. of Rate or fraction hours in thereof worker jobs/hour M. alone for x hours 1 x J. alone for y hours 1 y M. and J. together for 1 hr 1 1 1 M. alone for 2 hours 2 M. and J. together for 1/3 hr 1/3 Fill in the rates in jobs/hour in the first two cases by dividing jobs done by the number of hours: No. of jobs No. of Rate or fraction hours in thereof worker jobs/hour M. alone for x hours 1 x 1/x J. alone for y hours 1 y 1/y M. and J. together for 1 hr 1 1 1 M. alone for 2 hours 2 M. and J. together for 1/3 hr 1/3 We can now fill in M's rate working alone for 2 hours as the same rate 1/x. We can also fill in the rate of them working together for 1/3 hour as the same 1 job/hour rate as when they work for 1 hour. No. of jobs No. of Rate or fraction hours in thereof worker jobs/hour M. alone for x hours 1 x 1/x J. alone for y hours 1 y 1/y M. and J. together for 1 hr 1 1 1 M. alone for 2 hours 2 1/x M. and J. together for 1/3 hr 1/3 1 Now we can fill in the no. of jobs or fraction thereof (actually fraction tereof) that M. did alone for 2 hours by multiplying her rate times her time (2 hours) getting 2/x. Similar we can fill in the fraction of a job that they did together in 1/3 hour by multiplying their combined rate 1 job/hour by 1/3 hour. No. of jobs No. of Rate or fraction hours in thereof worker jobs/hour M. alone for x hours 1 x 1/x J. alone for y hours 1 y 1/y M. and J. together for 1 hr 1 1 1 M. alone for 2 hours 2/x 2 1/x M. and J. together for 1/3 hr 1/3 1/3 1 Our two equations come from: + = + = or + = + = Solve that system and get x = 3 and y = or 1.5 hours So Mary takes 3 hourse to do the job and Jane takes 1.5 hours Edwin