Who's old now and who is MEMORYLESS?
I still think that the point of this problem was to highlight the memoryless property.
That's why I would have assigned it.
It shows that finding lambda is unnecessary.
But .... are these rhetorical question ....? I'm tempted to say that the answer to both is you - the latter because you've clearly forgotten what the reaction of a typical student would be to your reply (assuming a student has been exposed to that property of the exponential distribution) .....
(But you're right, I should have included it as a throw away footnote ....)