SOLUTION: Together Maria and Johannes can pick a bushel of apples in 16 min. Maria takes 4 min more to pick a bushel than Johannes does. Find the time it takes each person to pick a bushel o

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Together Maria and Johannes can pick a bushel of apples in 16 min. Maria takes 4 min more to pick a bushel than Johannes does. Find the time it takes each person to pick a bushel o      Log On


   

Question 429340: Together Maria and Johannes can pick a bushel of apples in 16 min. Maria takes 4 min more to pick a bushel than Johannes does. Find the time it takes each person to pick a bushel of apples alone.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Together Maria and Johannes can pick a bushel of apples in 16 min.
Maria takes 4 min more to pick a bushel than Johannes does.
Find the time it takes each person to pick a bushel of apples alone.
:
Let m = time for Maria to pick a bushel alone
then
(m-4) = time for Joan to do it
:
Let the completed job = 1 (a bushel of apples
:
Each girl will pick a fraction of a bushel and the two fractions must equal 1
16%2Fm + 16%2F%28%28m-4%29%29 = 1
:
Multiply by m(m-4), results:
16(m-4) + 16m = m(m-4)
:
16m - 64 + 16m = m^2 - 4m
combine like terms on the right
0 = m^2 - 4m - 32m + 64
A quadratic equation
m^2 - 36m + 64 = 0
This will not factor, use the quadratic formula: a=1; b=-36; c=64
m+=+%28-%28-36%29+%2B-+sqrt%28-36%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+
Do the math here, two solutions but only one will be reasonable, about 34 min for Marie