Question 1134548
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution by the tutor @ankor@dixie-net.com is &nbsp;<U>WRONG</U>.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;What is even worst, &nbsp;it is &nbsp;<U>CONCEPTUALLY</U> &nbsp;wrong, &nbsp;which means that the idea of the solution is wrong. 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The right solution should use the conceptions of velocities (rates) and rate ratios.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;See my solution below.



<pre>
Let  {{{V[E]}}}  be the Ed's rate, in miles per hour;

     {{{V[F]}}}  be the Faith's rate,  and

     {{{V[M]}}}  be the Matt rate.


Since in a two-mile race, Ed can beat Faith by {{{1/5}}} = 0.2 of a mile, it means that the ratio of their rates is  {{{V[E]/V[F]}}} = {{{2/(2-0.2)}}} = {{{2/1.8}}}.


    It is totally clear: in that time as Ed will complete the 2 miles race, Faith will cover only 2-0.2 = 1.8 miles.



Next, since in a two-mile race, Faith can beat Math by {{{1/10}}} = 0.1 of a mile, it means that the ratio of their rates is  {{{V[F]/V[M]}}} = {{{2/(2-0.1)}}} = {{{2/1.9}}}.


It implies that the ratio of the rates  {{{V[E]/V[M]}}} = {{{(V[E]/V[F])*(V[F]/V[M])}}} = {{{(2/1.8)*(2/1.9)}}} = {{{4/(1.8*1.9)}}} = {{{2/(((1.8*1.9)/2))}}} = {{{2/1.71}}}.


It means that in the 2 miles race Ed can beat Matt by  2 - 1.71 = 0.29 miles.    <U>ANSWER</U>
</pre>

Solved.