Question

un excursionist parcurge in 4 zile astfel: in prima zi parcurge0,(4) din drum,a 2 a zi parcurge 0,(3) din rest iar in a 3 a zi parcurge 0,(6) din noul rest,ramanandu i pt a 4 a zi(ultima) de parcurs ultimii 60 km.Care este lungimea intregului drum?
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Answer 1

Răspuns:

Explicație pas cu pas:

Fie x km este lungimea intregului traseu.

$\dfrac{4}{9}*x,~(I~zi)\\x-\dfrac{4}{9}*x=x*(1-\dfrac{4}{9})=\dfrac{5}{9}*x,~(restul~dupa~I~zi)\\\dfrac{3}{9}* \dfrac{5}{9}*x=\dfrac{5}{27}*x,~(II~zi)\\\dfrac{5}{9}*x- \dfrac{5}{27}*x=x*(\dfrac{5}{9}-\dfrac{5}{27})=\dfrac{10}{27}*x,~(restul~dupa~II~zi)\\\dfrac{6}{9}*\dfrac{10}{27}*x=\dfrac{20}{81}*x,~(III~zi)\\\dfrac{10}{27}*x-\dfrac{20}{81}*x=x*(\dfrac{10}{27}-\dfrac{20}{81})=\dfrac{10}{81}*x,~restul~dupa~III~zi)\\Deci~\dfrac{10}{81}*x=60,~~x=60:\dfrac{10}{81}$

$x=60*\frac{81}{10}=81*6=486km$