Question 818633: A car travels 200 mi. A second car, traveling 10mph faster than the first car, makes the same trip in one hour less time. Find the speed of each car.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! D = 200
s = d / t
d = s * t
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car a:
T = time for car a
200 = sT
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car b:
200 = (s + 10)(T - 1)
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sT = (s + 10)(T - 1)
sT = sT - s + 10T - 10
s = 10T - 10
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200 = sT
200 = (10T - 10)T
10TT - 10T - 200 = 0
10T^2 - 10T - 200 = 0
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the above quadratic equation is in standard form, with a=10, b=-10, and c=-200
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to solve the quadratic equation, by using the quadratic formula, plug this:
10 -10 -200
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two solutions), of the quadratic are:
T = 5
T = -4
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the negative root doesn't make sense for time, so use the positive root:
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T = 5
s = 10T - 10
s = 10(5) - 10
s = 40
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answer:
speed of car a: 40 mph
speed of car b: 50 mph
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