Together 6519

One worker makes 15 parts per hour, the other 12, and the third 10. How many hours did each work when they worked together for 15 hours?

Correct answer:

a =  4 h
b =  5 h
c =  6 h

Step-by-step explanation:


a+b+c = 15
a·15 = b·12
b·12 = c·10

a+b+c = 15
15a-12b = 0
12b-10c = 0

Pivot: Row 1 ↔ Row 2
15a-12b = 0
a+b+c = 15
12b-10c = 0

Row 2 - 1/15 · Row 1 → Row 2
15a-12b = 0
1.8b+c = 15
12b-10c = 0

Pivot: Row 2 ↔ Row 3
15a-12b = 0
12b-10c = 0
1.8b+c = 15

Row 3 - 1.8/12 · Row 2 → Row 3
15a-12b = 0
12b-10c = 0
2.5c = 15


c = 15/2.5 = 6
b = 0+10c/12 = 0+10 · 6/12 = 5
a = 0+12b/15 = 0+12 · 5/15 = 4

a = 4
b = 5
c = 6

Our linear equations calculator calculates it.
b=5=5 h
c=6=6 h

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