# Machines

In the workshop are three machines. The first is treated 250 parts for 4.7 hours, the second is treated 300 parts for 1.9 hours and the third is treated 230 parts for 4.6 hours.

How long will take to make 3100 parts if worked all three machines at the same time?

Result

t =  11.87 h

#### Solution:

$v_1 = 250/4.7 = 53.1915 \ 1/h \ \\ v_2 = 300/1.9 = 157.8947 \ 1/h \ \\ v_3 = 230/4.6 = 50 \ 1/h \ \\ \ \\ v_1t +v_2t + v_3 t = 3100 \ \\ \ \\ t(v_1+v_2 + v_3 ) = 3100 \ \\ t = 3100 / 261.0862 \ \\ t = 11.87 \ \text{h}$

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