SOLUTION: It takes my father 3h tpo plow our cornfield with his new tractor. Using the old tractor, it takes me 5h. If we both plow for 1h before I go to school, how long will it take him to

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: It takes my father 3h tpo plow our cornfield with his new tractor. Using the old tractor, it takes me 5h. If we both plow for 1h before I go to school, how long will it take him to      Log On


   

Question 133571: It takes my father 3h tpo plow our cornfield with his new tractor. Using the old tractor, it takes me 5h. If we both plow for 1h before I go to school, how long will it take him to finish the plowing?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add the rates of plowing with the 2 tractors
(1 field / 3 hrs) + (1 field / 5 hrs) = (x fraction of field / 1 hr)
1%2F3+%2B+1%2F5+=+x%2F1
multiply both sides by 3%2A5
5+%2B+3+=+15x
x+=+8%2F15
This is the fraction of a field they plow
together before school. There is 1+-+%288%2F15%29+=+7%2F15
left for father to finish alone
Let t = hours for father to plow 7%2F15 of a field
1%2F3+=+%287%2F15%29%2Ft
This is just (father's rate = father's rate)
multiply both sides by t
%281%2F3%29%2At+=+7%2F15
multiply both sides by 15
5t+=+7
t+=+7%2F5 hrs
This is 1 and 2%2F5 hrs or
1 hours and 24 minutes for father to finish plowing the field