Math Is Fun Forum

satgur

Member

Registered: 2007-05-09

Posts: 2

Math Puzzle problem with looping

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.

What is the mathematical equation used to solve this problem?
Will Jack have to eat 100 apples? 
How many apples does Jack have at the end?  How many oranges does Bob have at the end?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Math Puzzle problem with looping

After n hours, Jack will have 5000 + 5n apples and Bob will have 300 + 30n oranges. The question is: is there an integer n such that 5000 + 5n = 300 + 30n? The answer is yes: n = 188. Therefore, after 188 hours of competition, Bob will have 5940 oranges and Jack (after eating the agreed number of apples) will have 5840 apples.

Last edited by JaneFairfax (2007-05-09 03:27:47)

satgur

Member

Registered: 2007-05-09

Posts: 2

Re: Math Puzzle problem with looping

Hi Jane,

Thanks for the reply. I will really appreciate if you can explain me mathematical equation you used to calculate the numbers.

Thanks
Satgur

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Math Puzzle problem with looping

In one hour, Jack produces 5 apples. Therefore in n hours, he will produce 5n apples. The total number of apples he will then have is 5000+5n. Similarly for Bob and his oranges.

Last edited by JaneFairfax (2007-05-09 04:29:41)