Question 360006
Sue is traveling 50 miles to an appointment she has to be to in 1 hour. After the first 30 miles she realizes she isn't going to make it and increases her speed by 15mph to get there on time. What was her speed for the first 30 miles?

let  her speed for 30 miles  be xmph
time taken = 30/x

speed increased to x+15 mph
time taken = 20/(x+5)
..
(30/x)+20/(x+5)=1
30(x+5)+20x / x(x+5)=1
30x+150+20x = x^2+5x
50x+150-x^2-5x=0
-x^2+45x+150=0
x^2-45x-150=0
solve using quadratic formula

discriminant = 2625
x1= (45+sqrt(2625))/2
x1=48.11 mph
x2 will be negative so ignore

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m.ananth@hotmail.ca