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balandron [24]
3 years ago
11

You can do one-half of a job in an hour. Your friend can do one-third of the same job in an hour. How long will it take to do th

e job if you work together? Write your answer as a decimal.
Mathematics
1 answer:
Mariana [72]3 years ago
5 0

You do:  1/2  job/hr

Your friend does:  1/3  job/hr

Together:       (1/2 + 1/3)  job / hr

                   = (3/6 + 2/6)  job/hr

                   =    5/6          job/hr .

Since you do  5/6 job/hr, the corresponding
inverse unit rate is 
                                 6/5  hr/job

                              = 1 and 1/5 hr/job

                              =  1.2 hours/job

                              = 1 hour 12 minutes  per job.

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<em>Additional comment</em>

If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.

A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).

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