Question

Un excursionist a parcurs un drum astfel: in prima zi 2 pe 5 din intregul drum si inca 18km, a doua zi 4 pe 9 din rest, a treia zi jumatate din noul rest, iar apoi in a patra zi ultimii 120 km. Care a fost lungimea drumului?

Answer 1

prima zi: 2/5·x +18km=2x/5 +18km;
a doua zi: 4/9(5x/5-2x/5-18)=4/9(3x/5-18)=4x/15-8;
a treia zi: 1/2·5/9(4x/15-8)=5/18(4x/15-8)=1/9·2x/3-40/18=2x/27-20/9=
(2x-60)/27;
a patra zi:1/2(2x-60)/27=(2x-60)/54=120km
⇒2x-60=6480
⇒2x=6540
⇒x=3270(km-lungimea traseului);

Answer 2

prima zi: 2/5·x +18km=2x/5 +18km;
a doua zi: 4/9(5x/5-2x/5-18)=
4/9(3x/5-18)=4x/15-8;
a treia zi: 1/2·5/9(4x/15-8)=
5/18(4x/15-8)=
1/9·2x/3-40/18=
2x/27-20/9=
(2x-60)/27;

a patra zi:1/2(2x-60)/27=
(2x-60)/54=120km
2x-60=6480
2x=6540
x=3270