it takes my father 3 hours to plow our cornfield with his new tractor using the old tractor it takes me 5 hours. if we both plow for 1 hour before i go to school, how long will it take dad to finish the plowing.
I got 2.5 hours but i think that is totally wrong?????
combined rate=field/3hrs + field/5hrs
time=field/(field/3 + field/5)
time= 15/(8)= less than your time.
To find the answer, we need to consider the rate at which each person plows the cornfield. Let's call your father's plowing rate "x" and your plowing rate "y".
We are given that it takes your father 3 hours (or x = 1/3) to plow the cornfield using his new tractor, and it takes you 5 hours (or y = 1/5) to plow using the old tractor.
If you both plow for 1 hour before you go to school, we need to calculate how much area you both can plow together in this time.
Your combined plowing rate per hour is (1/x) + (1/y) = (1/3) + (1/5) = 8/15.
Therefore, in 1 hour, you and your father can plow 8/15 of the cornfield.
Now we need to find out how much is left to plow after you leave for school. Let's call the remaining portion of the cornfield R.
R = 1 - (8/15) = 7/15.
The remaining 7/15 of the cornfield needs to be plowed by your father alone.
Since your father's plowing rate is x = 1/3, we can set up the equation:
(1/3) * T = 7/15,
where T represents the time it will take your father to finish plowing the remaining portion of the cornfield.
By solving the equation, we can find T:
T = (7/15) / (1/3) = (7/15) * (3/1) = 7/5 = 1.4 hours.
Hence, it will take your father approximately 1.4 hours, or 1 hour and 24 minutes, to finish plowing the cornfield after you leave for school.