Question

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 ?

Answer 1

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

Answer 2

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