Un biciclist parcurge in prima zi 1 supra 4 din drum , a doua zi parcurge 1 supra 3 din rest , iar a treia zi 1 supra 2 din noul rest . In a patra zi parcurge restul de 120 km . Ce lungime are drumul ?

x-lungimea drumului
I zi: x-x/4=(4x-x)/4=3x/4
II zi: 3x/4-1/3·3x/4=3x/4-x/4=2x/4=x/2
III zi: x/2-1/2·x/2=x/2-x/4=(2x-x)/4=x/4
x/4=120
x=120·4
x=480 km lungimea drumului
verificare
I zi :480x1/4=120
480-120=360
II zi : 360x1/3=120
360-120=240
III zi: 240x1/2=120
240-120=120

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Hasliulala Hasliulala · Answer 2 · 2015-01-10T21:36:27+02:00

Hasliulala Hasliulala

10-01-2015

x=lungime drum
I=[tex] \frac{x}{4} [/tex]
II=x- [tex] \frac{x}{4}= \frac{3x}{4} [/tex]
[tex] \frac{1}{3} * \frac{3x}{4} = \frac{3x}{12} [/tex]
III= [tex] \frac{3x}{4} - \frac{3x}{12} = \frac{6x}{12} [/tex]
[tex] \frac{1}{2} * \frac{6x}{12} = \frac{6x}{24} [/tex]
IV= 120 km
[tex] \frac{x}{4} + \frac{3x}{12} + \frac{6x}{24} + 120 =x[/tex] * numitorul comun 24*
6x+6x+6x+2880=24x
18x+2880=24x
2880=24x-18x=6x
x=2880:6=480 km

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