SOLUTION: A pilot flies a distance of 600 km. He could fly the same distance in 30 minutes less time by increasing his average speed by 40 km/hr. Find his actual average speed.

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Question 792516: A pilot flies a distance of 600 km. He could fly the same
distance in 30 minutes less time by increasing his average speed by
40 km/hr. Find his actual average speed.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A pilot flies a distance of 600 km. He could fly the same
distance in 30 minutes less time by increasing his average speed by
40 km/hr. Find his actual average speed.
-----------------
r = lower speed
r*t = 600 --> t = 600/r
(r+40)*(t-0.5) = 600
-----
Sub for t in the 2nd eqn
(r+40)*(600/r - 0.5) = 600
600 - 0.5r + 24000/r - 20 = 600
-0.5r + 24000/r = 20
-r + 48000/r = 40
r^2 - 48000 + 40r = 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=193600 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 200, -240. Here's your graph:

==============
r = 200 km/hr
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