Question

Un biciclist parcurge distanta dintre doua orase in patru zile. In prima zi parcurge o cincime din drum plus 10 km, in a doua zi trei zecimi din rest, a treia zi doua septimi din rest plus 12 km, iar in a patra zi parcurge restul de 83 km. Ce distanta este intre cele doua localitati ?

Answer 1

ziua 1 =d/5 + 10km  
4d/5 - 10
ziua 2=3/10 ·(4d/5 - 10)
6d/25 - 3
4d/5-10 - 6d/25 + 3
14d/25 - 7
ziua 3 =2/7 ·(14d/25 - 7) +12 
4d/25 +10
8d/25 - 7 - 4d/25 -10
4d/25 - 17
ziua 4  = 4d/25 - 17 = 83 de aici rezulta ca  
4d/25 = 100   
d = 100·25/4    
d = 625 km

Answer 2

x=lungime drum
x/5+10=ziua 1
x-x/5-10=4x/5-10=rest
(4x/5-10)× 3/10=6x/25-3=ziua 2
4x/5-10-6x/25+3=14x/25-7=rest
(14x/25-7)×2/7+12=4x/25-2+12=4x/25+10=ziua 3
x/5+10+6x/25-3+4x/25+10+83=x
x/5+6x/25+4x/25+100=x
5x+6x+4x+2500=25x
10x=2500
x=250 km