MO Z9–I–3 - 2017

Robots Robert and Hubert assemble and disassemble coffee grinders. Each of them assembles a grinder four times faster than he disassembles one himself. When they came to the workshop in the morning, several grinders were already assembled there. At 7:00 Hubert started to assemble and Robert to disassemble, exactly at 12:00 Hubert finished assembling one grinder and Robert finished disassembling another. In total during this shift 70 grinders were added. At 13:00 Robert started to assemble and Hubert to disassemble, exactly at 22:00 Robert finished assembling the last grinder and Hubert finished disassembling another. In total during this shift 36 grinders were added. How long would it take them to assemble 360 grinders if Robert and Hubert were assembling them together?

Final Answer:

h =  8
r =  16
t =  15 h

Step-by-step explanation:


70 = (r-h/4)·(12.00-7.00)
36 = (h-r/4)·(22.00-13.00)

5h-20r = -280
36h-9r = 144

Pivot: Row 1 ↔ Row 2
36h-9r = 144
5h-20r = -280

Row 2 - 5/36 · Row 1 → Row 2
36h-9r = 144
-18.75r = -300


r = -300/-18.75 = 16
h = 144+9r/36 = 144+9 · 16/36 = 8

h = 8
r = 16

Our linear equations calculator calculates it.
t=360/(r+h)=360/(16+8)=15 h



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