Question 1206391
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ron can trim 10 trees in 2/3 the time it takes tony. they trim trees together for 1 hour 11 minutes. 
then tony continues alone until a total of 10 trees are trimmed ( it took him 35 minutes and 30 seconds). 
working alone, how long would it take ron to trim 10 trees?
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<pre>
Let's "a" be the Tony's rate of work, in terms of the entire job per minute.

Then Ron's rate of work is 1.5a of the entire job per minute.



They worked together for 1 hour and 11 minutes, which is 71 minutes.

After that, Tony worked alone for 35.5 minutes .



So, we write the joint work equation in the form

    (a+1.5a)*71 + 35.5*a = 1.


At this point, the setup is complete.
Now our task is to solve this equation and find "a".


    2.5a*71 + (71/2)*a = 1


Multiply both sides by 2

    5a*71   + a*71 = 2

    6a*71 = 2

    a = {{{2/(6*71)}}} = {{{1/(3*71)}}} = {{{1/213}}}.


Thus, the Tony's rate of work is  {{{1/213}}}  of the job per minute.

So, Tony needs  213 minutes to complete the job working alone.

Hence, Ron needs {{{(2/3)*213}}} minutes = 2*71 minutes = 142 minutes, or 2 hours and 22 minutes

to complete the job working alone.


<U>ANSWER</U>.  Ron needs 2 hours and 22 minutes to complete the job working alone.
</pre>

Solved.


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The solution by the tutor ankor@dixie-net.com is incorrect.


I did not try to identify his error explicitly, but definitely, that solution is incorrect.