Answer:
[tex]15\text{ mph}[/tex]
Step-by-step explanation:
GIVEN: Ken and Joe leave their apartment to go to a football game [tex]45\text{ miles}[/tex] away. Ken drives his car [tex]30\text{ mph}[/tex] faster than Joe can ride his bike.
TO FIND: If it takes Joe [tex]2\text{ hours}[/tex] longer than Ken to get to the game, what is Joe’s speed.
SOLUTION:
Let the speed of joe be [tex]x\text{ mph}[/tex]
Speed of Ken [tex]=(x+30)\text{ mph}[/tex]
Total distance to go to football game [tex]=45\text{ miles}[/tex]
As
[tex]Time=\frac{Distance}{Speed}[/tex]
Total time taken by Joe is [tex]2\text{ hours}[/tex] longer than Ken.
[tex]\frac{45}{x}=\frac{45}{(x+30)}+2[/tex]
[tex]\frac{45}{x}=\frac{45+2(x+30)}{(x+30)}[/tex]
[tex]45(x+30)=x(105+2x)[/tex]
[tex]2x^2+60x-1350=0[/tex]
[tex]x=-70,15[/tex]
[tex]x=15\text{ mph}[/tex]
hence speed of joe is [tex]15\text{ mph}[/tex]
