# Passenger 16583

At 7:00 AM, a truck left town A at a speed of 40 km/h. Opposite him, a passenger car left town B at 8:30 AM at a speed of 70 km/h. The distance between cities A and B is 225 km. At what distance from city A will the two cars compete?

x =  120 km

### Step-by-step explanation:

x+y= 225
x = 40·(t-7.00)
y = 70·(t-8.5)

x+y = 225
40t-x = 280
70t-y = 595

Pivot: Row 1 ↔ Row 3
70t-y = 595
40t-x = 280
x+y = 225

Row 2 - 40/70 · Row 1 → Row 2
70t-y = 595
-x+0.571y = -60
x+y = 225

Row 3 + Row 2 → Row 3
70t-y = 595
-x+0.571y = -60
1.571y = 165

y = 165/1.57142857 = 105
x = -60-0.57142857142857y/-1 = -60-0.57142857 · 105/-1 = 120
t = 595+y/70 = 595+105/70 = 10

t = 10
x = 120
y = 105

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