# The hiker

The hiker will travel 40% of the route on the first day 1and/3 of the rest of the second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day?

a =  30
b =  15
c =  30
t =  75

### Step-by-step explanation:

a+b+c=t
a = 40/100t
b = 1/3·(t-a)
c = 30

a+b+c=t
a = 40/100·t
b = 1/3·(t-a)
c = 30

a+b+c-t = 0
100a-40t = 0
a+3b-t = 0
c = 30

Pivot: Row 1 ↔ Row 2
100a-40t = 0
a+b+c-t = 0
a+3b-t = 0
c = 30

Row 2 - 1/100 · Row 1 → Row 2
100a-40t = 0
b+c-0.6t = 0
a+3b-t = 0
c = 30

Row 3 - 1/100 · Row 1 → Row 3
100a-40t = 0
b+c-0.6t = 0
3b-0.6t = 0
c = 30

Pivot: Row 2 ↔ Row 3
100a-40t = 0
3b-0.6t = 0
b+c-0.6t = 0
c = 30

Row 3 - 1/3 · Row 2 → Row 3
100a-40t = 0
3b-0.6t = 0
c-0.4t = 0
c = 30

Row 4 - Row 3 → Row 4
100a-40t = 0
3b-0.6t = 0
c-0.4t = 0
0.4t = 30

t = 30/0.4 = 75
c = 0+0.4t = 0+0.4 · 75 = 30
b = 0+0.6t/3 = 0+0.6 · 75/3 = 15
a = 0+40t/100 = 0+40 · 75/100 = 30

a = 30
b = 15
c = 30
t = 75

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