SOLUTION: 3. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Question 155378: 3. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 3

Let x = original speed (ie slower speed)

Start with the distance-rate-time formula

Plug in and

Divide both sides by "x" to isolate "t"

The statement "if he had gone 10mph faster, the trip would have taken 1 hour less" tells us that the new speed is and the new time is

Go back to the distance-rate-time formula

Plug in , , and replace with

FOIL

Plug in

Multiply

Multiply every term by the LCD "x" to clear the denominator

Subtract 200x from both sides

Combine like terms

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

Since a negative speed doesn't make sense, this means that the only solution is

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Answer:

So the original speed was 40 mph

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