Let Jean's speed while running = x mph
Then Jean's speed while riding will be = x+9 mph
Distance covered by running = 8 miles
Distance covered by riding = 11 miles
Total time taken to complete the race = 1.5 hours
As, [tex]time=\frac{distance}{speed}[/tex]
So, time for running= [tex]\frac{8}{x}[/tex]
And time for riding= [tex]\frac{11}{x+9}[/tex]
Equation becomes:
[tex]\frac{8}{x}+\frac{11}{x+9}=1.5[/tex]
Now, multiply every term by 2x(x+9) to clear denominators:
[tex]16(x+9)+22x=3x(x+9)[/tex]
Simplifying it we get
[tex]3x^{2}-11x-144=0[/tex]
Solve the quadratic equation using formula
[tex]x= \frac{-b+\sqrt{b^{2}-4ac }}{2a}[/tex]
putting a=3 , b= -11, c= -144
we get (x - 9)(3x + 16) = 0
where x=9 and x=[tex]\frac{-16}{3}[/tex]
Neglect the negative answer as speed cannot be negative, so x = 9 mph
Hence, Jean's running speed is 9 mph and riding speed is x+9 = 9+9 = 18 mph
