SOLUTION: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Mem

Algebra ->  Customizable Word Problem Solvers  -> Evaluation -> SOLUTION: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Mem      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 433248: Marty drove his fully loaded moving van 270 miles to Memphis. With his van empty, Marty drove 15 mi/h faster and made the return trip in 1.5 hours less. Find the speed going to Memphis.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
If Marty's speed is set equal to x, then:
270/x=(270/(x+15))+1.5
Multiply all by x(x+15), we get:
270(x+15)=270x+1.5(x2+15x)
270x+4050=270x+1.5x2+22.5x
0=1.5x2+22.5x-4050
Divide by 1.5:
0=x2+15x-2700
0=(x+60)(x-45)
x=-60,45
Throwing out the negative result, we get Marty's speed to Memphis as 45mph.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B15x%2B-2700+=+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=%2815%29%5E2-4%2A1%2A-2700=11025.

Discriminant d=11025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-15%2B-sqrt%28+11025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+11025+%29%29%2F2%5C1+=+45
x%5B2%5D+=+%28-%2815%29-sqrt%28+11025+%29%29%2F2%5C1+=+-60

Quadratic expression 1x%5E2%2B15x%2B-2700 can be factored:
1x%5E2%2B15x%2B-2700+=+1%28x-45%29%2A%28x--60%29
Again, the answer is: 45, -60. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B15%2Ax%2B-2700+%29