Question 459347
A car travels 360 miles at a certain speed. If the speed had been 5mph faster the trip would have been made in 1 hr less time. Find the speed. 
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Let s = the speed of the car
Let t = the original time
Then the time to travel the 360 miles is:
t = 360/s
If the speed were 5 mph faster, the time [in hrs] would have been:
t - 1 = 360/(s+5)
Using the value for t in the 1st equation gives:
360/s - 1 = 360/(s+5)
Solve for s:
(360 - s)/s = 360/(s+5)
360s + 360*5 - s^2 - 5s = 360s
s^2 + 5s - 1800 = 0
{{{s = (-5 +- sqrt(25+4*1800))/2}}}
Take the positive solution.
s = (-5 + 85)/2 = 40
So the speed of the car is 40 mph