SOLUTION: The speed of an ordinary train is x km/hr and that of an express train is x+25 km/hr. (i) Find the time taken for each train to cover 300 km. (ii) If the ordinary tran takes 2 hrs

Question 927846: The speed of an ordinary train is x km/hr and that of an express train is x+25 km/hr. (i) Find the time taken for each train to cover 300 km. (ii) If the ordinary tran takes 2 hrs more than the express train; calculate the speed of the express train.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
s = d/t
t = d/s
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time for ordinary train:
a = 300/x
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time for express train:
b = 300/(x+25)
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a = b + 2
300/x = 300/(x+25) + 2
300/x - 300/(x+25) = 2
(x+25)300/x(x+25) - 300x/x(x+25) = 2
(x+25)300 - 300x = 2x(x+25)
300x + 25*300 - 300x = 2xx + 50x
2xx + 50x - 7500 = 0
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the above quadratic equation is in standard form, with a=2, b=50 and c=-7500
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 50 -7500
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 = 50
x = -75
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the negative root doesn't fit the problem statement, so use the positive root:
x = 50
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answer:
speed of the express train = 50 + 25 = 75 kph
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