Respuesta :
ANSWER :
Jeff's speed is 12 mph
EXPLANATION :
The football game is 54 miles from their apartment.
Ian drives 24 mph faster than Jeff,
so if Jeff's speed is x,
Ian's speed will be x + 24
It takes 3 hours longer than Ian to get to the game,
so if Ian takes y hours to get to the game,
Jeff's time will be y + 3
Recall the equation of speed, time and distance.
[tex]d=rt[/tex]where d = distance
r = speed
t = time
Equation for Jeff :
[tex]54=x(y+3)[/tex]Equation for Ian :
[tex]54=(x+24)(y)[/tex]Express Jeff's equation as x in terms of y.
[tex]x=\frac{54}{y+3}[/tex]Substitute this to Ian's equation :
[tex]\begin{gathered} 54=(x+24)(y) \\ 54=(\frac{54}{y+3}+24)(y) \\ 54=\frac{54y}{y+3}+24y \\ \text{ Cross multiply :} \\ 54(y+3)=54y+24y(y+3) \\ 54y+162=54y+24y^2+72y \\ 0=24y^2+54y+72y-54y-162 \\ 0=24y^2+72y-162 \\ \text{ Divide the equation by 6 :} \\ 0=4y^2+12y-27 \\ 4y^2+12y-27=0 \\ (2x-3)(2x+9)=0 \end{gathered}[/tex]Equate the factors to 0.
2x - 3 = 0
2x = 3
x = 3/2
2x + 9 = 0
2x = -9
x = -9/2
Note that there's no negative time, so we will consider x = 3/2 only
Substitute x = 3/2 to Jeff's equation :
[tex]\begin{gathered} 54=x(y+3) \\ 54=x(\frac{3}{2}+3) \\ 54=x(\frac{9}{2}) \\ 108=9x \\ x=\frac{108}{9} \\ x=12 \end{gathered}[/tex]