How does time work on hourly rate?

[malvolio]

The contact may say "130 days from 1st April", but this is unlikely.

Indeed. However 90% of the time the client manager's budget submission to his financial authority to approve the spend will have been worded exactly like that - "I require n days effort at a maximum £x per day". That gives a maximum value of the contract to the agency who then take off their margin and divide the reminder by a round number of days to get the offered day rate. Not forgetting of course that most of the time the value of £x above has been set by the agencies themselves via the "normal market rate for the job" on the open market. Confusing, isn't it...

The bathroom building analogy still holds - if you hire a plumber you ask "How much to completely build this bathroom", you don't ask "What is the maximum whole number of weeks it will take and how much do you charge a week". And the difference between the two, where the latter is used because nobody knows the answer to "How long", is the difference between a contractor role and a pseudo permie one.