# Shari drove for 90 miles in the city. When she got on the highway, she increased her speed by 20 mph and drove for 130 miles. If Shari drove a total of 4 hours, how fast did she drive in the city?

Dec 11, 2016

45 mph

#### Explanation:

Let's call her speed in the city $x$ mph
Speed is miles per hour -speed=$\frac{\mathrm{di} s \tan c e}{t i m e}$
Rearranged
Time = $\frac{\mathrm{di} s \tan c e}{s p e e d}$

So in the city the time is $\frac{90}{x}$
After the time is 130/(x+20
The total time is 4 hours
So $\frac{90}{x} + \frac{130}{x + 20} = 4$
The common denominator is $x \left(x + 20\right)$
So $\frac{90 \left(x + 20\right) + 130 x}{x \left(x + 20\right)} = 4$
$\frac{90 x + 1800 + 130 x}{{x}^{2} + 20 x} = 4$
$220 x + 1800 = 4 \left({x}^{2} + 20 x\right)$
Divide through by 4
$55 x + 450 = {x}^{2} + 20 x$
${x}^{2} - 35 x - 450 = 0$
Factorise
$\left(x - 45\right) \left(x + 10\right) = 0$
So $x = 45$
Check it out 90 miles at 45mph plus 130 miles at 65 mph is 4 hours