SOLUTION: Tricia drove 1,400 miles from her home to Dallas. On the way back home, she averaged 6 miles per hour more, and the drive back home took her 3 hours less. Find Tricia's average spe

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Tricia drove 1,400 miles from her home to Dallas. On the way back home, she averaged 6 miles per hour more, and the drive back home took her 3 hours less. Find Tricia's average spe      Log On

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Question 996366: Tricia drove 1,400 miles from her home to Dallas. On the way back home, she averaged 6 miles per hour more, and the drive back home took her 3 hours less. Find Tricia's average speed on the way to Dallas.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Let r be speed going to dallas
let t be time going to dallas
Other known given variables
system%28k=3%2Cd=1400%2Cj=6%29
Generalized data table according to variables described
          speed   time     distance
TO         r       t        d
FROM      r+j      t-k      d

Uniform Travel Rate rule works like RT=D relating speed, time, distance. You want to form a system of equations and solve for the value of r, or a formula for r and then evaluate.

System should be, if keeping all in symbols,
system%28rt=d%2C%28r%2Bj%29%28t-k%29=d%29

Working through the system, you should obtain highlight%28kr%5E2%2Bjkr-jd=0%29, from which you can get a formula for r. (You may also find that substituting the given values into the quadratic equation now may give a fairly easy equation to deal with or maybe/maybe-not factorize).

Substituting for the given numbers now and simplifying in fact gives the quadratic highlight%28r%5E2%2B6r-2800=0%29. Go from that.
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Formula for general solution for quadratic equation will accordingly give
highlight%28highlight%28r=%28-6%2B106%29%2F2%29%29, the PLUS-form.