# Cyclist

Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target?

x =  45 km

### Step-by-step explanation:

a = 2/5 t
b = a-5
b = 3/8 t
x = t - a - b

a = 2/5·t
b = a-5
b = 3/8·t
x = t - a - b

5a-2t = 0
a-b = 5
8b-3t = 0
a+b-t+x = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-2t = 0
-b+0.4t = 5
8b-3t = 0
a+b-t+x = 0

Row 4 - 1/5 · Row 1 → Row 4
5a-2t = 0
-b+0.4t = 5
8b-3t = 0
b-0.6t+x = 0

Pivot: Row 2 ↔ Row 3
5a-2t = 0
8b-3t = 0
-b+0.4t = 5
b-0.6t+x = 0

Row 3 - -1/8 · Row 2 → Row 3
5a-2t = 0
8b-3t = 0
0.025t = 5
b-0.6t+x = 0

Row 4 - 1/8 · Row 2 → Row 4
5a-2t = 0
8b-3t = 0
0.025t = 5
-0.225t+x = 0

Pivot: Row 3 ↔ Row 4
5a-2t = 0
8b-3t = 0
-0.225t+x = 0
0.025t = 5

Row 4 - 0.025/-0.225 · Row 3 → Row 4
5a-2t = 0
8b-3t = 0
-0.225t+x = 0
0.1111x = 5

x = 5/0.11111111 = 45
t = 0-x/-0.225 = 0-45/-0.225 = 200
b = 0+3t/8 = 0+3 · 200/8 = 75
a = 0+2t/5 = 0+2 · 200/5 = 80

a = 80
b = 75
t = 200
x = 45

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