设甲车间有X人,乙车间有Y人.(X,Y都是大于0的自然数)
(5/6)X+(7/11)Y=70;
55X+42Y=4620;
Y=110-(55/42)X.
若X=42,则Y=110-(55/42)*42=110-55=55;
若X=84,则Y=110-(55/42)*84=0.(舍去)
所以,甲车间有42人,乙车间有55人.