Question 271607
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Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd behind her. 
The girls then repeated the race, with Yolanda starting 10-yd behind the starting line. 
If each girl ran at the same rate as before, who won the race? By how many yards?
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        In his post, @mananth presented a formal solution.

        This solution is correct and, generally speaking,  it is good.


        But this problem admits much simpler mental solution,  based on reasoning.

        If you will master it,  you will understand the situation much better.



<B>Solution</B>


According to the problem, Yolanda ran 100 yards in the same time as Yoko ran 90 yards.

It is the same as to say that Yolanda ran every 10 yards in the same time as Yoko ran every 9 yards.


So, when Yolanda ran 110 yards (11 times 10 yards), Yoko ran 11 times 9 yards, i.e. 99 yards.


It means, that in the second scenario, Youlanda will finish when Yoko will be 1 yard before the finish line.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solved mentally and completely in &nbsp;4 &nbsp;lines, &nbsp;making the solution &nbsp;TRANSPARENT 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and understandable/accessible for a &nbsp;4-the grade student

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;without using any equations and without using any expressions.