allegansveritatem
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- Jan 10, 2018
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Here is problem:
56. A car travels for 125 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take 1 hour less time. What is the car's rate of speed?
Here is what I did with it:
. . . . .\(\displaystyle \dfrac{125}{x}\, -\, 1\, =\, \dfrac{125}{x\, +\, 5}\)
. . . . .\(\displaystyle 125x\, +\, 625\, -\, x^2\, -\, 5x\, =\, 125x\)
. . . . .\(\displaystyle 120x\, +\, 625\, -\, x^2\, =\, 125x\)
. . . . .\(\displaystyle 0\, =\, x^2\, +\, 5x\, -\, 625\)
Now, I am constrained to solve this by factoring--I haven't gotten to the chapters that teach other methods of solving quqadratic equations. My question is: Have I set this up wrong? If not, then, can this equation be factored? I can't seem to find the way. Looks prime to me.
56. A car travels for 125 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take 1 hour less time. What is the car's rate of speed?
Here is what I did with it:
. . . . .\(\displaystyle \dfrac{125}{x}\, -\, 1\, =\, \dfrac{125}{x\, +\, 5}\)
. . . . .\(\displaystyle 125x\, +\, 625\, -\, x^2\, -\, 5x\, =\, 125x\)
. . . . .\(\displaystyle 120x\, +\, 625\, -\, x^2\, =\, 125x\)
. . . . .\(\displaystyle 0\, =\, x^2\, +\, 5x\, -\, 625\)
Now, I am constrained to solve this by factoring--I haven't gotten to the chapters that teach other methods of solving quqadratic equations. My question is: Have I set this up wrong? If not, then, can this equation be factored? I can't seem to find the way. Looks prime to me.
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