SOLUTION: AN AIRPLANE FLYING EAST AT THE RATE OF 6 MILES/MINUTES ,PASSED OVER A COURT-HOUSE AT 2 PM. A SECOND PLANE FLYING NORTH AT THE RATE OF 6 MILES/MINUTES,PASSED OVER THE COURT-HOUSE AT

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Question 1109935: AN AIRPLANE FLYING EAST AT THE RATE OF 6 MILES/MINUTES ,PASSED OVER A COURT-HOUSE AT 2 PM. A SECOND PLANE FLYING NORTH AT THE RATE OF 6 MILES/MINUTES,PASSED OVER THE COURT-HOUSE AT 2:04 PM.IV THE PLANES ARE FLYING AT THE SAME ALTITUDE ,IN HOW MANY MINUTES AFTER 2 PM WILL THEY BE 36 MILES APART?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
AN AIRPLANE FLYING EAST AT THE RATE OF 6 MILES/MINUTES ,PASSED OVER A COURT-HOUSE AT 2 PM. A SECOND PLANE FLYING NORTH AT THE RATE OF 6 MILES/MINUTES,PASSED OVER THE COURT-HOUSE AT 2:04 PM. IV THE PLANES ARE FLYING AT THE SAME ALTITUDE,IN HOW MANY MINUTES AFTER 2 PM WILL THEY BE 36 MILES APART?
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p = distance of the 1st plane from the courthouse at t minutes past 2
q = distance of the 2nd plane from the courthouse at t minutes past 2
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t=0 at 2:04
p = 6t + 4*6 = 6t+24
q = 6t
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(6t+24)^2 + (6t)^2 = 36^2
(t+4)^2 + (t)^2 = 36
2t^2 + 8t -20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B8x%2B-20+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A2%2A-20=224.

Discriminant d=224 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+224+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+224+%29%29%2F2%5C2+=+1.74165738677394
x%5B2%5D+=+%28-%288%29-sqrt%28+224+%29%29%2F2%5C2+=+-5.74165738677394

Quadratic expression 2x%5E2%2B8x%2B-20 can be factored:
2x%5E2%2B8x%2B-20+=+%28x-1.74165738677394%29%2A%28x--5.74165738677394%29
Again, the answer is: 1.74165738677394, -5.74165738677394. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B-20+%29

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t =~ 1.74 minutes past 2:04
--> 5.74 minutes past 2:00