Good Work If You Can Get It
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.
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?
Getting Started
Teachers' Resources
Why do this problem?
This problem encourages students to think of different ways in which it can be solved. This can be done using trial and improvement, but preferably, and more efficiently, by creating some linear equations. The very fact that the six men have names beginning with the letters A to F should make an algebraic solution stand out!
Possible approach
Key questions
Possible extension
Learners could follow-up with this harder problem, How Many Miles to Go?
Possible support
Suggest making a table and tackle the problem using trial and improvement.