# Train from Prague

The first train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. How many hours and how far from cities with trains meet if the distance of cities is 400 km.

Result

t = 12:13 h
p =  168.8889 km
o =  231.1111 km

### Step-by-step explanation:

p+o = 400
p = 40(t-8)
o = 80(t-(9+20/60))

p+o = 400
p = 40·(t-8)
o = 80·(t-(9+20/60))

o+p = 400
p-40t = -320
60o-4800t = -44800

Pivot: Row 1 ↔ Row 3
60o-4800t = -44800
p-40t = -320
o+p = 400

Row 3 - 1/60 · Row 1 → Row 3
60o-4800t = -44800
p-40t = -320
p+80t = 1146.667

Row 3 - Row 2 → Row 3
60o-4800t = -44800
p-40t = -320
120t = 1466.667

t = 1466.66666667/120 = 12.22222222
p = -320+40t = -320+40 · 12.22222222 = 168.88888889
o = -44800+4800t/60 = -44800+4800 · 12.22222222/60 = 231.11111111

o = 2080/9 ≈ 231.111111
p = 1520/9 ≈ 168.888889
t = 110/9 ≈ 12.222222

Our linear equations calculator calculates it.

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