Given,
The distance, D = 240 miles
The average speed was 11 miles per hour.
Solution:
Let x be the speed.
Then, (x+11) will be the average speed.
The time taken to cover outward bound is
[tex]Time=\frac{240}{\left(x+11\right)}hrs......\lparen1)[/tex]
The time taken to cover homeward bound is
[tex]Time=\frac{240}{x}\text{ hrs......\lparen2\rparen}[/tex]
Add both equations (1) and (2)
[tex]\begin{gathered} Time\text{ + Time = 8 hrs} \\ \frac{240}{\left(x+11\right)}+\frac{240}{x}=8 \\ \frac{240x+240\left(x+11\right)}{x\left(x+11\right)}=8 \\ \frac{240x+240x+2,640}{x\left(x+11\right)}=8 \end{gathered}[/tex][tex]\begin{gathered} 480x+2640=8\lparen x^2+11x) \\ 480x+2640=8x^2+88x \\ 8x^2+88x-480x-2640=0 \\ 8x^2-392x-2640=0 \end{gathered}[/tex]
Divide the equation by 5.
[tex]\begin{gathered} x^2-49x-330=0 \\ x^2+6x-55x-330=0 \\ x\left(x+6\right)-55\left(x+6\right)=0 \\ \lparen x+6)\left(x-55\right)=0 \end{gathered}[/tex]
Thus, the value of x is
[tex]x=55,-6[/tex]
Justin's average speed to his parents house is 55 mph.
Justin's average speed from his parent's house is
[tex]\begin{gathered} x+11=55+11 \\ =66\text{ mph} \end{gathered}[/tex]
