Question

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?

Answer 1

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