Let x miles per hour be the speed Alexandra drove to the soccer game. Then she spent [tex]\dfrac{42}{x}[/tex] hours to drive to the soccer game.
On the way back, due to road construction she had to drive 21 miles per hour slower, then her speed is x-21 miles per hour and she spent [tex]\dfrac{42}{x-21}[/tex] hours.
Road back took 1 hour longer, then
[tex]\dfrac{42}{x-21}-\dfrac{42}{x}=1.[/tex]
Solve this equation:
[tex]\dfrac{42(x)-42(x-21)}{x(x-21)}=1,\\ \\42x-42x+882=x^2-21x,\\ \\x^2-21x-882=0,\\ \\D=(-21)^2-4\cdot (-882)=63^2,\ \sqrt{D}=63,\\ \\x_1=\dfrac{21-63}{2}=-21,\ x_2=\dfrac{21+63}{2}=42\ mi/h.[/tex]
Answer: 42 miles per hour
