# 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, a volume of 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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