Extend your stay

[Helen]

Test No. errors/advan-5 "At the Airport", question 7

We were having such an enjoyable time on our holiday that we visited our travel agent at the airport and asked whether it would be possible to lengthen our stay by another week.

(a) enjoyable
(b) visited
(c) whether
(d) lengthen

Test No. errors/advan-5 "At the Airport", answer 7

We were having such an enjoyable time on our holiday that we visited our travel agent at the airport and asked whether it would be possible to extend our stay by another week.

Correct entry: extend
The error was: (d) lengthen

You have not found the error.
We were having such an enjoyable time on our holiday that we visited our travel agent at the airport and asked whether it would be possible to lengthen our stay by another week.
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Preposition problem : can't one extend a stay FOR another week?

[Alan]

Neither is wrong and both are acceptable.
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English as a Second Language
You can read my ESL story Adverbs

[Guest]

and i made it 'prolong' here