SOLUTION: 3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle. i think it is 30mph but I canno

Question 199563: 3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
i think it is 30mph but I cannot figure out the equation
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, the distance-rate-time formula is

Since he "traveled 150 miles at a certain speed", this means that the first equation is (simply plug in d=150)

The statement "Had gone 20mph faster, the trip would have taken 2 hour less", tells us that the next equation is (the distance is the same, but the speed is now 20 mph faster and the time is 2 hours shorter)

The goal is to use this system to solve for "r" (and if we want, "t" also)

Start with the first equation.

Divide both sides by r.

Rearrange the equation

Move onto the second equation.

Plug in

FOIL

Multiply EVERY term by the LCD to clear out the fraction.

Subtract from both sides.

Combine and rearrange the terms.

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

Let's use the quadratic formula to solve for "r":

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 solutions are or

Since a negative speed doesn't make any sense, this means that we must ignore

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Answer:

So the only solution is which means that he was traveling 30 mph. So you are correct, good job.
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