Answer
50mph
Work Step by Step
Person traveled at speed $x$ for 250 miles. And then traveled at speed $x+10$ for 360 miles. The entire trip took 11 hours. Solve for X.
So lets make this a formula:
$\frac{250}{x}+ \frac{360}{x+10} = 11$
We need a common denominator so our first fraction lets multiply by $\frac{x+10}{x+10}$ so we get:
$\frac{250x+2500}{x^2 + 10x}+ \frac{360}{x+10} = 11$
Then to match, the second fraction we multiply by $\frac{x}{x}$ and we get:
$\frac{250x+2500}{x^2 + 10x}+ \frac{360x}{x^2+10x} = 11$
Now multiply both sides by $x^2+10x$ then reduce to one side
$250x + 2500 + 360x = 11x^2+110x$
$610x + 2500 = 11x^2 + 110x$
$610x = 11x^2 + 110x - 2500$
$0 = 11x^2 -500x - 2500$
Now we plug this into the quadratic formula:
$x = \frac{500\frac{+}{-}\sqrt (-500^2-(4*11*-2500))}{2*11}$
$x = \frac{500\frac{+}{-}\sqrt (250000+110000)}{22}$
$x = \frac{500\frac{+}{-}\sqrt (360000)}{22}$
$x = \frac{500\frac{+}{-}\sqrt (360000)}{22}$
$x = \frac{500\frac{+}{-}1100}{22}$
So we get two answers from this. $50$ and $-27.2727$. This answer requires a positive number so we get 50.
Let's confirm our answer:
$\frac{250}{50} + \frac{360}{50+10} = 11$
$5 + 6 = 11$
$11 = 11$
Perfect!
