SOLUTION: A man drives 108 km at an average rate. If he had driven 5 km/hr. faster, he would have made the trip in 15 hours less time. How fast did he drive?

Question 160148: A man drives 108 km at an average rate. If he had driven 5 km/hr. faster, he would have made the trip in 15 hours less time. How fast did he drive?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=his rate over the 108 km
And r+5=his rate if he had driven 5 km/hr faster
Time it takes at the rate of r=108/r
Time it takes him at the rate of r+5=108/(r+5)
Now we are told that (108/r)-15=108/(r+5) multiply each term by r(r+5)
108(r+5)-15r(r+5)=108r get rid of parens and simplify
108r+540-15r^2-75r=108r subtract 108r from each side
108r-108r+540-15r^2-75r=108r-108r collect like terms
-15r^2-75r+540=0 divide each term by -15
r^2+5r-36=0 ----quadratic in standard form and it can be factored
(r+9)(r-4)=0
r+9=0
r=-9-------discount negative value for r
and
r-4=0
r=4 km/hr----------------------ans
CK
108/4 -15=108/9
27-15=12
12=12
Hope this helps---ptaylor

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