Josemicelli was right.  I made a mistake before so I reposted it correctly in
my other pseudo-name AnlytcPhil:

Michael can do a job 2 hours faster than Dennis. Together they can complete the work in 5 hours. How long would it take Michael to do the job alone? 
(Round your answer to the nearest tenth of an hour.) 
Instead of a "D=RT" problem, this is a "J=RT" problem. "Jobs" instead of "Distance"

We put in 1 job for all three situations:

                                  Jobs      =     Rate      *    Time
                                              [In jobs/hr]     [In hrs.]  
-------------------------------------------------------------------------
Michael when working alone          1                             
Dennis when working alone           1                             
Michael & Dennis working together   1
Michael can do a job 2 hours faster than Dennis.
So we put t for Dennis' time, and t-2 for Michael's time because Michael 
take 2 LESS hours than Dennis.

                                  Jobs      =     Rate      *    Time
                                              [In jobs/hr]     [In hrs.]  
-------------------------------------------------------------------------
Michael when working alone          1                            t-2 
Dennis when working alone           1                             t
Michael & Dennis working together   1

Then we fill in the rates using R=J/T like we fill in R=D/T in other problems.  

                                  Jobs      =     Rate      *    Time
                                          [In jobs/hr]     [In hrs.]  
-------------------------------------------------------------------------
Michael when working alone          1            1/(t-2)         t-2 
Dennis when working alone           1             1/t             t
Michael & Dennis working together   1
Together they can complete the work in 5 hours.
When they work together, their rate is the sum of their individual rates,
so we express this sum by putting + between them.  Then we fill in 5 for 
the number of hours working together.

                                  Jobs      =     Rate      *    Time
                                             [In jobs/hr]     [In hrs.]  
-------------------------------------------------------------------------
Michael when working alone          1            1/(t-2)         t-2 
Dennis when working alone           1             1/t             t
Michael & Dennis working together   1         1/(t-2) + 1/t       5

Then we use JOBS = RATE × TIME

                                    1  =     [1/(t-2) + 1/t]  ×   5



Distribute



Multiply through by LCD of t(t-2)









 

 





 

 





Two answers:

t = 11.1 hours and 0.9 hours

We must discard Dennis taking only 0.9 hours because Michael's time
to do it would then be negative.  So we discard t=2.

So Dennis' time to do it alone is 11.1 hours.  Therefore Michael can do the 
job in 2 hours less, so Michael can do the job in 9.1 hours.

Edwin
 

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 "... 2 hours faster …" is nonsensical.

… in 2 hours less time... makes sense.

========================

I can run 10 mi/hr.

I can run 2 hours faster than that.

----------------

Hours is a measure of time.

Fast is an indication of speed, not time.



 

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
 Question asks time for Michael by himself.





, Michael's rate

, Dennis'es rate

, combined rate for both





 

RELATED QUESTIONS

Michael can do a job 3 hours faster than Dennis. Together they can complete the work in 8  (answered by BlGDAVE,josgarithmetic)

it takes mary 3 hours more to do a job than it takes jane. if they work together,they can  (answered by josmiceli)

John can complete a job alone in 2 hours, and it takes Tim 3 hours to do the same job... (answered by josmiceli)

Koko can paint a room two hours less than Andre. If they will work together, they can... (answered by Edwin McCravy)

Aly can paint a room two hours less than AJ. If they will work together, they can finish... (answered by josgarithmetic)

Bert can clean the sidewalks around the building in 2 hours in using a blower. Dennis can  (answered by richwmiller)

Allen can do a job 5 times faster than Billy. Billy can do the same job in 8 hours. How... (answered by josgarithmetic)

Allen can do a job 5 times faster than Billy. Billy can do the same job in 8 hours. How... (answered by josgarithmetic,greenestamps,Edwin McCravy,math_tutor2020)

Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can... (answered by josmiceli)