She rationalised being late by saying she had to work overtime.

rationalised 是动词 rationalise 的过去式形式。rationalise 由词根 rational（理性的）加上后缀 -ise（使...化）构成，意思是"使合理化"或"为...找合理借口"。在这里表示"试图用看似合理的理由来解释自己的行为"。