SOLUTION: Roland traveled from Nashville to St. Louis, a distance of 300 miles. If he had increased his speed by 10 mph he would have arrived at St. Louis an hour and 30 minutes sooner. Wha

Question 60997: Roland traveled from Nashville to St. Louis, a distance of 300 miles. If he had increased his speed by 10 mph he would have arrived at St. Louis an hour and 30 minutes sooner. What was his speed?
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
300=rt or r=300/t
300=(r+10)(t-1.5) now substitute (300/t) for r in the second equation we get
300=(300/t+10)(t-1.5)
300=(300/t*t)+10*t+(300/t*-1.5)+(10*-1.5)
300=300+10t-450/t-15
0=10t-450/t-15
0=(10t^2-450-15t)/t
0=10t^2-15t-450
(5t+30)(2t-15)=0
5t+30=0
5t=-30
t=-30/5
t=-6
2t-15=0
2t=15
t=15/2
t=7.5 hours then
300=r*7.5
r=300/7.5
r=40 mph speed of trip

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