Correct. The boys' individual rates, in cords per hour, are $\displaystyle\frac{{1}}{{10}}\usepackage{cmbright}\Huge\$ , $\displaystyle\frac{{1}}{{12}}\usepackage{cmbright}\Huge\$ , and $\displaystyle\frac{{1}}{{15}}\usepackage{cmbright}\Huge\$ . Together their rate, in cords per hour, is

$\displaystyle\frac{{1}}{{10}}+\frac{{1}}{{12}}+\frac{{1}}{{15}}=\frac{{6}}{{60}}+\frac{{5}}{{60}}+\frac{{4}}{{60}}=\frac{{15}}{{60}}=\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$

If together they can chop 1 cord in t hours, then: $\displaystyle\frac{{1}}{{4}}=\frac{{1}}{{t}}\usepackage{cmbright}\Huge\$ , which leads to $\displaystyle{t}={4}\usepackage{cmbright}\Huge\$ .