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

Answer:

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