Question

Un calator a parcurs un drum astfel 1/3 din drum in prima zi , a doua zi 2/3 din rest ,a treia zi 3/5 din noul rest, a patra zi 4/5 din ce a mai ramas, iar a cincea ultimii 12 km . Aflati lungimea drumului .

Answer 1

x-lungimea drumului
I zi :   x-x/3=(3x-x)/3=2x/3
II zi:   2x/3-2/3·2x/3=2x/3-4x/9=(6x-4x)/9=2x/9
III zi   2x/9-3/5·2x/9=2x/9-2x/15=(10x-6x)/45=4x/45
IV zi   4x/45-4/5·4x/45=4x/45-16x/225=(20x-16x)/225=4x/225
4x/225=12
4x=12·225
4x=2700
x=2700/4
x=675 km

I zi:   675·1/3=225
II zi   (675-225)·2/3=450·2/3=300
III zi:  (450-300)·3/5=150·3/5=90
IV zi :  (150-90)·4/5=60·4/5=48
V zi     12
225+300+90+48+12=675

Succes!