# Pumps

The first pump flows 16 liters per second into the basin by the second pump 75% of the first and by the third pump half more than the second. How long will it take to fill the basin with all three pumps simultaneously, volume 15 m3 (cubic meters)?

x =  326 s

### Step-by-step explanation:

a = 16
b = 0.75 · a
c = 1.5 · b
16 x + 0.75· 16 · x + (0.75· 16 ·x)(1+1/2) = 15·1000

a = 16
b = 0.75 · a
c = 1.5 · b
16·x + 0.75· 16 · x + (0.75· 16 ·x)·(1+1/2) = 15·1000

a = 16
0.75a-b = 0
1.5b-c = 0
92x = 30000

Row 2 - 0.75 · Row 1 → Row 2
a = 16
-b = -12
1.5b-c = 0
92x = 30000

Pivot: Row 2 ↔ Row 3
a = 16
1.5b-c = 0
-b = -12
92x = 30000

Row 3 - -1/1.5 · Row 2 → Row 3
a = 16
1.5b-c = 0
-0.6667c = -12
92x = 30000

x = 30000/92 = 326.08695652
c = -12/-0.66666667 = 18
b = 0+c/1.5 = 0+18/1.5 = 12
a = 16/1 = 16

a = 16
b = 12
c = 18
x = 7500/23 ≈ 326.086957

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