Correct. Their individual rates, in dumplings per hour, are as follows:

$\displaystyle\frac{\text{1,000}}{{4}}\usepackage{cmbright}\Huge\$ , $\displaystyle\frac{\text{1,000}}{{6}}\usepackage{cmbright}\Huge\$ , and $\displaystyle\frac{\text{1,000}}{{12}}\usepackage{cmbright}\Huge\$

Together their rate, in dumplings per hour, is the following:

$\displaystyle\frac{\text{1,000}}{{4}}+\frac{\text{1,000}}{{6}}+\frac{\text{1,000}}{{12}}=\frac{\text{3,000}}{{12}}+\frac{\text{2,000}}{{12}}+\frac{\text{1,000}}{{12}}=\frac{\text{6,000}}{{12}}={500}\usepackage{cmbright}\Huge\$

If together they can make 1,000 dumplings in t hours, then: $\displaystyle{500}=\frac{\text{1,000}}{{t}}\usepackage{cmbright}\Huge\$ , which leads to $\displaystyle{t}={2}\usepackage{cmbright}\Huge\$ .