SOLUTION: A Monorail car traves 100 miles in 50 minutes less time than it takes and automobile to travel the same distance. Find the speeds of the two vehicles if the monorail goes 20 mph fa

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Question 94481: A Monorail car traves 100 miles in 50 minutes less time than it takes and automobile to travel the same distance. Find the speeds of the two vehicles if the monorail goes 20 mph faster than the automobiles.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A Monorail car travels 100 miles, in 50 minutes less time than it takes and automobile to travel the same distance. Find the speeds of the two vehicles if the monorail goes 20 mph faster than the automobiles.
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Let s = speed of the auto
Then
(s+20) = speed of the monorail
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Change 50 min to hr: 50/60 = 5/6 hr
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Write a time equation, time = dist/speed
:
Auto time - mono time = 5%2F6hr
100%2Fs - 100%2F%28%28s%2B20%29%29 = 5%2F6
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Get rid of the denominators, multiply equation by 6s(s+20)
6(s+20)(100) - 6s(100) = s(s+20)(5)
:
(6s + 120)(100) - 600s = 5(s^2+ 20s)
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600s + 12000 - 600s = 5s^2 + 100s
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0 = 5s^2 + 100s - 12000
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Simplify the quadratic equation, divide by 5
s^2 + 20s - 2400 = 0
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Factors to:
(s + 60)(s - 40) = 0
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s = +40; it's the positive solution we want here
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Auto speed: 40 mph, monorail speed: 60 mph
:
:
Check our solutions
100/40 - 100/60 =
2.5 - 1.667 = .8333 which is 5/6
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