# Long bridge

Roman walked on the bridge. When he heard the whistle, he turned and saw Kamil running at the beginning of the bridge. They would meet in the middle of the bridge if he went to him. Roman rushed and did not want to waste time returning 150m. He continued walking, and Kamil caught up with him at the end of the bridge. How long was the bridge?

x =  900 m

### Step-by-step explanation:

x = a+b
a -150 = x/2
a + 2·150 = x

a+b-x = 0
2a-x = 300
a-x = -300

Pivot: Row 1 ↔ Row 2
2a-x = 300
a+b-x = 0
a-x = -300

Row 2 - 1/2 · Row 1 → Row 2
2a-x = 300
b-0.5x = -150
a-x = -300

Row 3 - 1/2 · Row 1 → Row 3
2a-x = 300
b-0.5x = -150
-0.5x = -450

x = -450/-0.5 = 900
b = -150+0.5x = -150+0.5 · 900 = 300
a = 300+x/2 = 300+900/2 = 600

a = 600
b = 300
x = 900

Our linear equations calculator calculates it.

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