Question

A car travels 120 mi averaging a certain speed. If the car had gone 10 mph​ faster, the trip would have taken 1 hr less. Find the​ car's average speed.

Answer 1

The average speed of a car will be "30 mph".

Step-by-step explanation:

The given values are:

Distance = 120 mi

Let the speed be "x".

As we know,

`Time = (Distance)/(Speed)`

`=(120)/(x)`

According to the question,

If the speed of a car = x + 10

then the time will be:

=
`(120)/(x) -1`

Now,

⇒
`Speed* Time=(x+10)((120)/(x)-1)`

⇒
`120=120+(1200)/(x) -x-10`

On multiplying "x" both sides, we get

⇒
`120x=120x+1200-x^2-10x`

⇒
`x^2+10x-1200`

⇒
`x^2+40x-30x-1200=0`

⇒
`x(x+40)-30(x+40)=0`

⇒
`(x+40)(x-30)=0`

`x+40=0`

`x=-40`

Or,

`x-30=0`

`x=30`

So that the average speed will be "30 mph".