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SaraP · Feb 9, 2011, 02:12 PM

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.

jcaron2 · Feb 9, 2011, 03:52 PM

You'll have two equations and two unknowns.

Both equations are of the form d=rt (distance = rate x time).

The two unknowns are Steve's speed (r) and the time it took him to travel (t).

You should write one equation for Steve's actual scenario, where he went 200 miles at a speed of r in time t. Your other equation should be for the other scenario, where he could have gone 200 miles at a speed of r+10 in a time of t-1.

Can you write down the equations and solve them now?

SaraP · Feb 10, 2011, 11:26 AM

Is it 200/x = 200/x + 10 -1
My answer is 20 mph. Is this right?

Unknown008 · Feb 10, 2011, 11:33 AM

No, your equation is wrong. It should be:

$\frac{200}{x} = \frac{200}{x+10} + 1$

The time on the left is larger (since the vehicle is going slower). So, to make both times equal, you need to add 1 hour to the right, which is a smaller time.

jcaron2 · Feb 10, 2011, 01:39 PM

Unknown008 is exactly right. You were very close, except that you subtracted 1 from the wrong side.

It might be less confusing if you write it in two separate equations (which may have been what you did in the first place. Maybe it was just a simple sign error - we all make those from time to time :) ):

200 = r * t (this represents Steve's actual trip)

200 = (r+10)*(t-1) (this represents the trip he would have taken if he had traveled faster)

Now we can solve the first equation for one of the variables so that we can plug that value into the second equation:

200 = r * t

$t = \frac{200}{r}$

Now if we plug this into the second equation, we get

200 = (r+10)*(t-1)

$200 = (r + 10)*(\frac{200}{r}-1)$

You can solve this any way you want, but notice that if you manipulate it just right, you get the exact equation Unknown008 came up with:

$200 = (r + 10)*(\frac{200}{r}-1)$

$\frac{200}{r+10} = \frac{200}{r}-1$

$\frac{200}{r+10} + 1 = \frac{200}{r}$

Note that this is a quadratic equation so you'll get two answers. One should be positive and one negative. Obviously, only the positive one is meaningful (since a negative rate would mean he got there in negative time).