Answer:
The average speed of a car will be "30 mph".
Explanation:
The given values are:
Distance = 120 mi
Let the speed be "x".
As we know,
[tex]Time = \frac{Distance}{Speed}[/tex]
[tex]=\frac{120}{x}[/tex]
According to the question,
If the speed of a car = x + 10
then the time will be:
= [tex]\frac{120}{x} -1[/tex]
Now,
⇒ [tex]Speed\times Time=(x+10)(\frac{120}{x}-1)[/tex]
⇒ [tex]120=120+\frac{1200}{x} -x-10[/tex]
On multiplying "x" both sides, we get
⇒ [tex]120x=120x+1200-x^2-10x[/tex]
⇒ [tex]x^2+10x-1200[/tex]
⇒ [tex]x^2+40x-30x-1200=0[/tex]
⇒ [tex]x(x+40)-30(x+40)=0[/tex]
⇒ [tex](x+40)(x-30)=0[/tex]
[tex]x+40=0[/tex]
[tex]x=-40[/tex]
Or,
[tex]x-30=0[/tex]
[tex]x=30[/tex]
So that the average speed will be "30 mph".
