SOLUTION: A car travels 200 miles. A second car travels 10 mph faster than the first car makes the same trip in one hour less time. Find the speed of each car.

Question 441191: A car travels 200 miles. A second car travels 10 mph faster than the first car makes the same trip in one hour less time. Find the speed of each car.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let v = the speed of car 1
Then v+10 = the speed of car 2
Let t = the travel time of car 1
Then t-1 = the travel time of car 2
Since speed = distance/time, for car 1 we can write:
v = 200/t [1]
And for car 2:
v + 10 = 200/(t - 1)
And since t = 200/v from equation [1], we have
v + 10 = 200/(200/v - 1)
Cross-multiply and solve for v:
(200/v - 1)(v + 10) = 200
Using FOIL we get
200 + 2000/v - v - 10 = 200
2000/v - v - 10 = 0
Multiply through by v:
2000 - v^2 - 10v = 0
Solve using quadratic formula:
v = (10 +- sqrt(100 + 8000))/-2
Take the positive solution:
v = 40
So the speed of car 1 is 40 mph; the speed of car 2 is 50 mph
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