Three machines

The power of the three machines is 2: 3: 5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours?

Correct result:

n =  1500

Solution:

p1=22+3+5=15=0.2 p2=3+52+3+5=45=0.8  h=400/p2=400/0.8=500  n=3⋅ h=3⋅ 500=1500p_{1}=\dfrac{ 2 }{ 2+3+5 }=\dfrac{ 1 }{ 5 }=0.2 \ \\ p_{2}=\dfrac{ 3+5 }{ 2+3+5 }=\dfrac{ 4 }{ 5 }=0.8 \ \\ \ \\ h=400 / p_{2}=400 / 0.8=500 \ \\ \ \\ n=3 \cdot \ h=3 \cdot \ 500=1500

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