# Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. How do you determine speed of the vehicle?

##### 2 Answers

Speed

#### Explanation:

Let

We are told that if he had traveled at a speed of

Since distance travelled

and

So we have

Using the quadratic formula

Since the speed must be non-negative,

The slower speed is 40 mph, the faster speed is 50 mph.

#### Explanation:

There are 2 different scenarios described here, Write an expression for the speed of each of them.

The difference between the times would be 1 hour. This allows us to make an equation.

Let the slower speed be

The faster speed is

At the slower speed, the time,

At the faster speed, the time,

(

The difference between the two times is 1 hour.

Multiply each term by

Find factors of 2000 which differ by 10.

The factors must be quite close to

We find

The slower speed is 40mph, the faster speed is 50 mph.