SOLUTION: Jack and Bob are farmers. Jack grows apples, Bob grows oranges. On May 9th, Jack has harvested 5000 apples, and Bob has harvested 300 oranges. However, Jack will harvest apples

Question 238674: Jack and Bob are farmers. Jack grows apples, Bob grows oranges. On May 9th, Jack has harvested 5000 apples, and Bob has harvested 300 oranges. However, Jack will harvest apples at a rate of 5/hr, and Bob will harvest oranges at a rate of 30/hr. If Jack and Bob eventually end up with the exact same number of fruits, Jack agreed to eat 100 apples, and both will stop harvesting. If Jack and Bob never end up with the exact same number of fruits, both will stop harvesting on the hour that Bob has more fruit than Jack.
8. What is the mathematical equation used to solve this problem?
9. Will Jack have to eat 100 apples?
10. How many apples does Jack have at the end? How many oranges does Bob have at the end?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Jack:

Bob:

If ever

exactly, then Jack eats the 100 apples.

However, since time is a continuous variable, no matter what the numbers are, so long as Bob's rate of harvesting is greater than Jack's and there is no specified time limit, Jack and Bob will always be equal at some point. Now, I suspect that you stated the problem incorrectly. I think you probably wanted to include the restriction that Jack and Bob have an equal harvest at an even hour. In fact, for this problem, this idea is moot because setting the two Right Hand Sides equal and solving for

has an integer result. You have to solve for this result and then substitute back into the original equations to answer the last question.

John

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