SOLUTION: If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive?

Question 68525This question is from textbook Algebra:Structure and Method
: If I increase my usual driving speed by 10 km/h, I can drive the 255 km trip to Nashville in 24 min less than usual. How fast do I usually drive? This question is from textbook Algebra:Structure and Method

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=usual driving speed
Then x+10=increased driving speed
Distance(d)=rate(r) times time(t) or d=rt and t=d/r
Time it takes at usual driving speed=255/x
Time it takes at increased speed=255/(x+10)
24 min=24/60 hr=0.4 hr
Now we are told that increased driving time plus 0.4 hr equals usual driving time. So our equation to solve is:
255/(x+10)+0.4=255/x multiply both sides by x(x+10)
255(x)(x+10)/(x+10)+(0.4)(x)(x+10)=255/(x+10)(x/x) clear fractions
255x+0.4x^2+4x=255x+2550 subtract 255x and 2550 from both sides
0.4x^2+4x-2550=0 divide by 0.4
x^2+10x-6375=0----------------------quadratic in standard form
This quadratic can be factored
(x+85)(x-75)=0
x=-85 km/h-----------------discount negative speed
and
x=75 km/h----------------------------usual speed
x+10=75+10=85 km/h-----------------------increased speed

ck
255/75=255/85+0.4
3.4=3.4

Hope this helps----ptaylor
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