SOLUTION: On​ Monday, Alberta picked the strawberry​ patch, and Ernie sold the berries. On​ Tuesday, Ernie picked and Alberta​ sold, but it took him 2 hours longer to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: On​ Monday, Alberta picked the strawberry​ patch, and Ernie sold the berries. On​ Tuesday, Ernie picked and Alberta​ sold, but it took him 2 hours longer to      Log On


   

Question 1089241: On​ Monday, Alberta picked the strawberry​ patch, and Ernie sold the berries. On​ Tuesday, Ernie picked and Alberta​ sold, but it took him 2 hours longer to get the berries picked than it took Alberta. On Wednesday they worked together and got all of the berries picked in 5 hours. How long did it take Ernie to pick the berries by​ himself? Find an exact answer and an approximate answer to the problem.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = Alberta's time in hrs to pick on monday
+t+%2B+2+ = Ernie's time in hrs to pick on tuesday
+5+ = their time in hrs picking together on wednesday
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I think what they are not telling you is that they need a
certain amount of berries each day, and they stop picking
when they get that amount. I can call that amount [ 1 load of berries ]
------------------------------------------------------------
Alberta's rate of picking:
[ 1 load of berries ] / [ t hrs ]
Ernie's rate of picking:
[ 1 load of berries ] / [ t + 2 hrs ]
Their rate of picking working together:
[ 1 load of berries ] / [ 5 hrs ]
-----------------------------------
Add their individual rates to get their rate working together
+1%2Ft+%2B+1%2F%28%28+t%2B2+%29%29+=+1%2F5+
Multiply each side by +5t%2A%28+t%2B2+%29+
+5%2A%28+t+%2B+2+%29+%2B+5t+=+t%2A%28+t+%2B+2+%29+
+5t+%2B+10+%2B+5t+=+t%5E2+%2B+2t+
+10t+%2B+10+=+t%5E2+%2B+2t+
+t%5E2+-+8t+-+10+=+0+
Complete the square
+t%5E2+-+8t+%2B+%28-8%2F2%29%5E2+=+10+%2B+%28-8%2F2%29%5E2+
+t%5E2+-+8t+%2B+16+=+10+%2B+16+
+%28+t+-+4+%29%5E2+=+%28+sqrt%2826%29+%29%5E2+
+t+-+4+=+sqrt%2826+%29+
+t+=+4+%2B+sqrt%28+26+%29+
This is Ernies exact time in hrs
+sqrt%2826%29+=+5.1+
+t+=+4+%2B+5.1+
+t+=+9.1+
Ernie's approximate time in hrs
---------------------------------
check the answer:
+1%2Ft+%2B+1%2F%28%28+t%2B2+%29%29+=+1%2F5+
+1%2F%28%28+4+%2B+sqrt%2826%29+%29%29+%2B+1%2F%28%28+6+%2B+sqrt%2826%29+%29%29+=+1%2F5+

+30+%2B+5%2Asqrt%2826%29+%2B+20+%2B+5%2Asqrt%2826%29+=+24+%2B+10%2Asqrt%2826%29+%2B+26+
+50+%2B+10%2Asqrt%2826%29+=+50+%2B+10%2Asqrt%2826%29+
OK
( you can check using +t+=+9.1+ also )