13.023. Identical parts are processed on two machines. The productivity of the first machine is $40 \%$ higher than that of the second. How many parts were processed during the shift on each machine, if the first machine worked for 6 hours during this shift, and the second - 8 hours, and both machines together processed 820 parts?
Solution.

Let the productivity of the second machine be $x$; then the productivity of the first machine is $1.4x$ parts per hour. The first machine processed $1.4x \cdot 6$ parts in the shift; the second machine processed $x \cdot 8$ parts. According to the condition, $1.4x \cdot 6 + x \cdot 8 = 820$, from which $x = 50$. Therefore, the first machine processed $1.4 \cdot 50 \cdot 6 = 420$ parts in the shift; the second machine processed $50 \cdot 8 = 400$ parts.

Answer: 420 and 400 parts.