Question 926561: A car travels for 100 miles at a uniform speed. If the speed is increased by 5 miles per hour, the trip would take one hour less time. What is the cars original speed?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = original speed
t = trip time at speed x
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s = d/t
t = d/s
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x = 100/t
t = 100/x
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x + 5 = 100/(t - 1)
(x + 5)(t - 1) = 100
(x + 5)(100/x - 1) = 100
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(x + 5)(100/x - 1) = 100
100 - x + 500/x - 5 = 100
-x + 500/x - 5 = 0
(-x + 500/x - 5 = 0)x
-xx + 500 - 5x = 0
-xx - 5x + 500 = 0
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the above quadratic equation is in standard form, with a=-1, b=-5 and c=500
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 -5 500
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = -25
x = 20
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
x = 20 mph
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Solve quadratic equations, quadratic formula:
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