SOLUTION: Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 70.46 miles apart. If one travels 9 miles per hour s

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Question 458479: Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 70.46 miles apart. If one travels 9 miles per hour slower than the other, what is the rate of the faster train?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
(2x)2+(2x+18)2=(70.46)2
4x2+4x2+72x+324=4964.6116
8x2+72x-4640.6116=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B72x%2B-4640.6116+=+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=%2872%29%5E2-4%2A8%2A-4640.6116=153683.5712.

Discriminant d=153683.5712 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-72%2B-sqrt%28+153683.5712+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2872%29%2Bsqrt%28+153683.5712+%29%29%2F2%5C8+=+20.0015601544065
x%5B2%5D+=+%28-%2872%29-sqrt%28+153683.5712+%29%29%2F2%5C8+=+-29.0015601544065

Quadratic expression 8x%5E2%2B72x%2B-4640.6116 can be factored:
8x%5E2%2B72x%2B-4640.6116+=+8%28x-20.0015601544065%29%2A%28x--29.0015601544065%29
Again, the answer is: 20.0015601544065, -29.0015601544065. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B72%2Ax%2B-4640.6116+%29

Throwing out the negative answer, we get the speed of the slower train to be 20.0015601544065 mph and the speed of the faster train to be 29.0015601544065 mph..