Question 1206391
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Answer:  <font color=red>142 minutes</font> (aka <font color=red>2 hours and 22 minutes</font>)


Short Explanation


Solve the equation 71/r + 106.5/(1.5r) = 1 to get r = <font color=red>142</font>
The 71 is from 60 + 11 = 71
The 106.5 is from adding an additional 35.5 min to 71.


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Longer Explanation


1 full job = trimming ten trees
Ron can do the job in 2/3 the time it takes Tony when working alone.
Reverse things to say that Tony can do the job in 3/2 the time it takes Ron when working alone.


3/2 = 1.5
r = time it takes for Ron to do the job when working alone
1.5r = time it takes for Tony to do the job when working alone
r > 0
Let's have each time value in minutes.


Ron has a unit rate of 1/r of a job per minute.
Tony has a unit rate of 1/(1.5r) = 2/(3r) of a job per minute.


Their combined unit rate is (1/r) + (2/(3r)) = 5/(3r) of a job per minute.
Caution: This assumes neither worker slows down the other.


They work together for 1 hr + 11 min = 60 min +11 min = 71 min.


rate*time = amount done
( 5/(3r) )*( 71 minutes) = 355/(3r) of a job



IF Ron and Tony got the job fully 100% done when working together, then 355/(3r) = 1 would be the case. 
Meaning they completed 1 full job.


However, Ron leaves early and the work isn't finished.
Therefore we know 355/(3r) is on the interval 0 < 355/(3r) < 1.


355/(3r) is the amount of the job done so far.
1 - (355/(3r)) = (3r - 355)/(3r) is the amount of the job still left to do after Ron leaves.
It might help to draw out a number line diagram.
Note the two fractions add to 1.



For Tony Only
rate*time = amount still needed to do
( 2/(3r) of a job per min )*( 35.5 min ) = (3r - 355)/(3r) of a job
( 2/(3r) )*( 35.5 ) = (3r - 355)/(3r)
71/(3r) = (3r - 355)/(3r)
71 = 3r - 355
3r = 71+355
3r = 426
r = 426/3
r = <font color=red>142</font>


Therefore, Ron needs <font color=red>142 minutes</font> when doing the entire job on his own.
Tony will need 1.5r = 1.5*142 = 213 minutes when doing the entire job on his own.


<font color=red>142 min</font> = 120 min + 22 min = <font color=red>2 hr + 22 min</font>
213 min = 180 min + 33 min = 3 hr + 33 min


When working together, they are able to do 5/6 of the job because of this scratch work
rate*time = amount done
(5/(3r))*(71) = (5/(3*142))*(71) = 5/6


This will mean Tony does the remaining 1/6 of the job on his own after Ron leaves.
note: (1/6)x = 35.5 solves to x = 213 to represent how long it takes Tony to do the job on his own, i.e. (1/6)*(1.5r) = 35.5 solves to r = <font color=red>142</font>


Edit: Tutors ikleyn and  greenestamps appear to have a more efficient approaches.
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