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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B40x%2B-48000+=+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=%2840%29%5E2-4%2A1%2A-48000=193600.

Discriminant d=193600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+193600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2840%29%2Bsqrt%28+193600+%29%29%2F2%5C1+=+200
x%5B2%5D+=+%28-%2840%29-sqrt%28+193600+%29%29%2F2%5C1+=+-240

Quadratic expression 1x%5E2%2B40x%2B-48000 can be factored:
1x%5E2%2B40x%2B-48000+=+%28x-200%29%2A%28x--240%29
Again, the answer is: 200, -240. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B40%2Ax%2B-48000+%29

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r = 200 km/hr