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Jim made a 450 mile trip in his car at a certain speed.
If he had gone 10 mph faster, he could have made the trip in one hour less time.
Find his speed.
Let s = that "certain speed"
(s+10) = the faster speed
Write a time equation; time = dist/speed
Actual time - faster time = 1 hr
multiply by s(s+10), results
450(s+10) - 450s = s(s+10)
450s + 4500 - 450s = s^2 + 10s
Arrange as quadratic equation on the right
0 = s^2 + 10s - 4500
Use the quadratic formula to find s
In this problem x=s, a=1, b=10 c=-4500
Two solutions, but we just want positive solution
s = 62.27 mph his actual speed
Check solution, find the time at each speed
450/62.27 = 7.2266 hrs
450/72.27 = 6.2266 hrs
difference: 1 hrs