# 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?

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 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(2048)   (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