Having seen that the Qt3 / Qt4 libraries overlap in all the Linux distributions I tried, I thought it would be nice to give a more complete answer to the solution to this problem. If you are using a debian-based distribution, the previously suggested answer for using dpkg might work; however, for example, on other Linux distributions such as Fedora, this will not work.
A more suitable solution, no matter which distribution you use, if you have alternatives installed, follow these steps:
update-alternatives --install /usr/bin/qmake qmake /usr/bin/qmake-qt4 10
Then, for good measure, you can follow this: update-alternatives --set qmake /usr/bin/qmake-qt4
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