SOLUTION: I need some assistance please. Two cities are 1000 miles apart. On the first flight a plane flew into a 50 mph headwind. On the return flight the plane had 50 mph tailwind. The

Algebra ->  Test -> SOLUTION: I need some assistance please. Two cities are 1000 miles apart. On the first flight a plane flew into a 50 mph headwind. On the return flight the plane had 50 mph tailwind. The       Log On


   

Question 873649: I need some assistance please.
Two cities are 1000 miles apart. On the first flight a plane flew into a 50 mph headwind. On the return flight the plane had 50 mph tailwind. The round trip flight was 4.5 hours. What is the average speed of the plane without the wind?
A. 480 mph
B. 450 mph
C. 375 mph
D. 325 mph
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

 t = D/r

1000%2F%28r-50%29+%2B+1000%2F%28r%2B50%29+=+9%2F2

     2000r%2F%28r%5E2+-+2500%29+=+9%2F2

 9r^2-2000r -22500 = 0,  r = 450 mph




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-4000x%2B-22500+=+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=%28-4000%29%5E2-4%2A9%2A-22500=16810000.

  

  Discriminant d=16810000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4000%2B-sqrt%28+16810000+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-4000%29%2Bsqrt%28+16810000+%29%29%2F2%5C9+=+450

    x%5B2%5D+=+%28-%28-4000%29-sqrt%28+16810000+%29%29%2F2%5C9+=+-5.55555555555556

    

    Quadratic expression 9x%5E2%2B-4000x%2B-22500 can be factored:

  9x%5E2%2B-4000x%2B-22500+=+9%28x-450%29%2A%28x--5.55555555555556%29

  Again, the answer is: 450, -5.55555555555556.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-4000%2Ax%2B-22500+%29