SOLUTION: A toy airplane flies according to the formula d(t)=5+20t-t^2 where d(t) is in meters and t is in seconds. How long will the toy airplane take to reach a distance of 100 meters from

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Question 1053466: A toy airplane flies according to the formula d(t)=5+20t-t^2 where d(t) is in meters and t is in seconds. How long will the toy airplane take to reach a distance of 100 meters from the person who controls it?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d%28t%29+=+-t%5E2+%2B+20t+%2B+5+
given:
+d%28t%29+=+100+
+100+=+-t%5E2+%2B+20t+%2B+5+
+-t%5E2+%2B+20t+-+95+=+0+
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+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+-1+
+b+=+20+
+c+=+-95+
+t+=+%28+-20+%2B-+sqrt%28+20%5E2-4%2A%28-1%29%2A%28-95%29+%29%29%2F%282%2A%28-1%29%29+
+t+=+%28+-20+%2B-+sqrt%28+400+-+380+%29%29%2F%28+%28-2%29+%29+
+t+=+%28+-20+%2B-+sqrt%28+20+%29%29%2F%28+%28-2%29+%29+
+t+=+%28+-20+-+4.472+%29+%2F+%28-2%29+
+t+=+24.472+%2F+2+
+t+=+12.236+
and also:
+t+=+%28+-20+%2B+4.472+%29%2F%28-2%29+
+t+=+15.528%2F2+
+t+=+7.764+
After 7.764 sec and 12.236 sec the toy plane is 100 m
from the controler
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Heres the plot:
+graph%28+500%2C+500%2C+-4%2C+40%2C+-15%2C+150%2C+-x%5E2+%2B+20x+%2B+5+%29+
Note that the peak is at +t+=+10+sec+ and +d+=+105+ m
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The times I came up with should be below and above +t+=+10+
by the same amount
+10+-+7.764+=+2.236+
and
+12.236+-+10+=+2.236+
OK