Question 135904: A car is driven 850 miles. If it had gone 5.0 miles per hour faster it would have made the trip in 2.0hr less time. What was the speed?
So far, I have this:
distance = rate x time
850 = r x t
t = 850/r
850 = (r+5)(t-2)
Answer by stumblefall(3)   (Show Source):
You can put this solution on YOUR website! You can use the word "speed" but the most common notations use "rate".
The distance is the one thing that is common to this whole thing. We are analyzing two scenarios: one goes a certain number of miles per hour (r) and takes a certain amount of time (t); the second goes 5 miles per hour more (r+5), and takes two hours less time (t-2). So your equation just needed to go one line further--you got that 850 = r x t and 850 = (s+5)(t-2); you just have to make one more jump to get
r x t = (r + 5) x (t - 2).
Because both equations are equal to 850, they are also equal to each other.
Now we can solve this:
rt = rt - 2r + 5t - 10 (using the FOIL method); subtract rt from both sides:
0 = -2r + 5t - 10
But t = 850 / r, so we get
0 = -2r + 4250 / r - 10
If we multiply both sides by r, we get
 ; switching the terms and dividing by -2, we get
At this point we will use the quadratic solution:
We can only factor a 25 out of 8525 to get
Our negative answer isn't going to mean anything, which leaves us with:
or
This is the actual answer, but to get an approximate answer, we will estimate the square root of 170 to be 18.4662. This gives us:
 or about 43.6655.
Plugging this back into the original equation shows us that a trip of 850 miles at 43.6655 miles per hour results in a trip length of about 19.47 hours. If we had done that same trip at 48.6655 miles per hour (five more), the trip would have taken about 17.47 hours, or two fewer.
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