Good work if you can get it

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



A job needs three men to work for two weeks ($10$ working days).

Andy works for all $10$ days.

Bert works for the first week and Clive works for the second week.

Dave works for $6$ days, but then is too sick to work.

Eddy takes his place for $3$ days, then Fred does the last day.

Image
Good Work If You Can Get It

When the job is finished they are all paid the same amount. At first they could not work out how much each man should have, but then Fred says:

"If I give my wages to Andy, and Eddy gives £$100$ to both Dave and me, then the wages will be correct".

How much was paid for the whole job, and how much does each man get?