# Cross-country race

In the charity cross-country race of three-member relays, each team had to run 36 km. Adam, Boris, and Ctirad gradually ran for team A. Boris and Ctirad ran a distance three times longer than Adam. Ctirad ran the length of 5 km longer than Boris.

How many km did Adam, Boris, and Ctirad run?

a =  9
b =  11
c =  16

### Step-by-step explanation:

a+b+c=36
b+c = 3a
c = 5 + b

a+b+c=36
b+c = 3·a
c = 5 + b

a+b+c = 36
3a-b-c = 0
b-c = -5

Pivot: Row 1 ↔ Row 2
3a-b-c = 0
a+b+c = 36
b-c = -5

Row 2 - 1/3 · Row 1 → Row 2
3a-b-c = 0
1.333b+1.333c = 36
b-c = -5

Row 3 - 1/1.33333333 · Row 2 → Row 3
3a-b-c = 0
1.333b+1.333c = 36
-2c = -32

c = -32/-2 = 16
b = 36-1.3333333333333c/1.33333333 = 36-1.33333333 · 16/1.33333333 = 11
a = 0+b+c/3 = 0+11+16/3 = 9

a = 9
b = 11
c = 16

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