A team of three men Andy, Boyd and Cole and a boy Jim are to collect some oranges from an orchard.

1. Jim can shake the oranges off the trees as fast as three men can together gather them.
2. Any one of Andy, Boyd and Cole can shake 5 oranges off the trees as fast as two of the men and Jim can gather 4 oranges.
3. Everyone worked the whole time in the most effective way, either shaking or gathering oranges.
4. The total payment received by the team was $500 and the money was disbursed based on how fast each member could shake and gather oranges.

Derive the amount of money received by each team member.

From 2, after some time, exactly 5 oranges will be shaken, and exactly 4 collected. Assuming the men each collect the same, and the boy at least collects something, they must collect 1 each and he must collect 2, to total 4.  So his collection rate is twice theirs.

He is also not as good at shaking, since despite the above, they can collect all the oranges he can shake in a given period.

So let's assign Jim to collection only, and assume that he can collect, say, 2 per minute. The men then collect 1 per minute, and shake 5 per minute. After an hour, say, Jim collects 120 oranges. It takes the men 8 minutes to shake that many oranges, leaving 52 minutes.  Their best strategy (given that all oranges are to be 'collected'- see first line of the puzzle) is to shake for 1/6 of that time, and collect for 5/6, ensuring every last orange is accounted for.

Jim collects 120 oranges. The men shake 250, and collect 130. Since both activities are essential, we assign the same value to an orange 'shake', and an orange 'collect', with 500 activities in all. Jim receives $120; the men share the remaining $380, the precise shares depending on who performed the final shake, and who collected the odd orange.

A completely different way to look at the whole problem is to have regard to the fact that all were fully occupied, and no labour was wasted by anyone. If so, since all worked for the same length of time, it does not seem unreasonable that each should receive $125.

   

Edited on July 23, 2014, 3:02 am

Posted by broll on 2014-07-23 02:50:57