SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.

Question 200501: Steve traveled 600 miles at a certain speed. Had he gone 20mph 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!

Remember, the distance-rate-time formula is

Since he "traveled 600 miles at a certain speed", this means that the first equation is

The statemtent "Had gone 20mph faster, the trip would have taken 1 hour less", tells us that the next equation is

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 the fractions.

Subtract from both sides.

Combine and rearrange the terms.

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.

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

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Answer:

So the speed of his vehicle is 100 mph

If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.
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