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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Together Maria and Johannes can pick a bushel of apples in 16 minutes. Maria takes 4 minutes more to pick a bushel than Johannes does. Find the time it takes each person to pick a       Log On


   

Question 593460: Together Maria and Johannes can pick a bushel of apples in 16 minutes. Maria takes 4 minutes more to pick a bushel than Johannes does. Find the time it takes each person to pick a bushel of apples alone.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their individual rates of picing to get
their rate of picking together
Together, rate = ( 1 bushel ) / ( 16 min )
Let +t+ = Johanne's time ion minutes to pick 1 bushel
+t+%2B+4+ = Maria's time in minutes to pick 1 bushel
--------------------------------
+1%2Ft+%2B+1%2F%28+t+%2B+4+%29+=+1%2F16+
Multiply both sides by +16t%2A%28+t+%2B+4+%29+
+16%2A%28+t+%2B+4+%29+%2B+16t+=+t%2A%28+t+%2B+4+%29+
+16t+%2B+64+%2B+16t+=+t%5E2+%2B+4t+
+t%5E2+-+32t+%2B+4t+-+64+=+0+
+t%5E2+-+28t+-+64+=+0+
Use quadratic formula
t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-28+
+c+=+-64+
+t+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2+-+4%2A1%2A%28-64%29+%29%29+%2F+%282%2A1%29+
+t+=+%28+28+%2B-+sqrt%28+784+%2B+256+%29%29+%2F+2+
+t+=+%28+28+%2B-+sqrt%28+1040+%29%29+%2F+2+
+t+=+%28+28+%2B+32.25%29+%2F+2+ ( using the (-) sqrt gives negative time: ignore )
+t+=+60.25%2F2+
+t+=+30.125+
+t+%2B+4+=+34.125+
Johanne takes 30.125 min picking alone
Maria takes 34.125 min picking alone
check:
+1%2Ft+%2B+1%2F%28+t+%2B+4+%29+=+1%2F16+
+1%2F30.125+%2B+1%2F34.125+=+1%2F16+
+.0332+%2B+.0293+=+.0625+
+.0625+=+.0625+
OK