SOLUTION: A farmer can plow a given field in 2 hours less time than it take his son. If they acquire two tractors and work together, they can plow the field in 5 hours. How long does I tak

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A farmer can plow a given field in 2 hours less time than it take his son. If they acquire two tractors and work together, they can plow the field in 5 hours. How long does I tak      Log On


   

Question 1132505: A farmer can plow a given field in 2 hours less time than it take his son. If they acquire two tractors and work together, they can plow the field in 5 hours. How long does I take the father alone?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Work with the fractions of the job each does in 1 hour.

Let x be the number of hours the farmer takes; then x+2 is the number of hours the son takes.

Then the fractions of the job each does in 1 hour are 1/x and 1/(x+2).

Together they take 5 hours to do the job; so together the fraction they do together is 1/5.

Then the equation is (fraction the farmer does in 1 hour) plus (fraction the son does in 1 hour) = (fraction they do together in 1 hour):

1%2Fx+%2B+1%2F%28x%2B2%29+=+1%2F5

Multiply everything by the least common denominator -- (5)(x)(x+2) -- to obtain a quadratic equation. The quadratic doesn't factor, so you will need to solve using the quadratic formula.