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=distancetime
Rearranged
Time = distancespeed

So in the city the time is 90x
After the time is 130x+20
The total time is 4 hours
So 90x+130x+20=4
The common denominator is x(x+20)
So 90(x+20)+130xx(x+20)=4
90x+1800+130xx2+20x=4
220x+1800=4(x2+20x)
Divide through by 4
55x+450=x2+20x
x235x450=0
Factorise
(x45)(x+10)=0
So x=45
Check it out 90 miles at 45mph plus 130 miles at 65 mph is 4 hours