If A farmer uses a large tractor,she can plow a filed in eight hours. Her sister, using a smaller tractor can plow the same field in 12 hrs. How many hours would it take to plow the field if they worked together ? Express your answer as a mixed number and show your work.

Question

If A farmer uses a large tractor,she can plow a filed in eight hours.  Her sister, using a smaller tractor can plow the same field in 12 hrs. How many hours would it take to plow the field if they worked together ? Express your answer as a mixed number and show your work.

Reiny · Answer

Here is a generic way to solve these type of problems

farmer's rate = job/8
Sister's rate = job/12

combined rate = job/8 + job/12
= 5job/24

so time for combinded rate = job/(5job/24)
= 24/5 or 4.8 hours.

notice "job" is just a phoney variable, it will cancel out anyway.