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

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) (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?
---------------
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
-----
t=0 at 2:04
p = 6t + 4*6 = 6t+24
q = 6t
---
(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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=224 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.74165738677394, -5.74165738677394. Here's your graph:

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

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