Question 1116402
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            The tutor @MathTherapy correctly noticed that there was a mistake in my previous solution to this problem.


            So I re-edit the solution.  Now what you see below is correct and corrected.


            Thanks to @MathTherapy !



<pre>
Let "t" be the time under the hypothetical scenario, in hours (the "if . . . " scenario).


Then your "speed" equation is this

{{{90/t}}} - {{{90/(t+1/6)}}} = {{{2/11}}}.    (1)


In this equation

    {{{90/(t+1/6)}}} is the regular speed (the basic scenario);

    {{{90/t}}} is the hypothetical speed (the "if . . . " scenario).

    {{{2/11}}} is the given difference of speeds;  {{{1/6}}} = {{{1/6}}} of an hour = 10 minutes.


Simplify eq(1):

{{{90/t}}} - {{{540/(6t+1)}}} = {{{2/11}}}


11*90*(6t+1) - 11*540*t = 2*t*(6t+1)


990 = 12t^2 + 2t,


12t^2 + 2t - 990 = 0


{{{t[1,2]}}} = {{{(-2 +- sqrt(2^2 + 4*12*990))/(2*12)}}} = {{{(-2 +- 218)/24}}}.


The only positive solution  is  t = {{{(-2 + 218)/24}}} = {{{216/24}}} = 9 hours.


Thus, the hypothetical scenario time is 9 hours, which means that the regular scenario time is 9 hours and 10 minutes.


<U>Answer</U>.  9 hours and 10 minutes.
</pre>

Solved.