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?

1 Answer
Dec 11, 2016

45 mph

Explanation:

Let's call her speed in the city x mph
Speed is miles per hour -speed=(distance)/(time)
Rearranged
Time = (distance)/(speed)

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