SOLUTION: a bullet train which is 40km/hr faster than the existing train will replace the existing train on an 850km journey. If the bullet train does the journey 3hours faster than the exis

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Question 1199: a bullet train which is 40km/hr faster than the existing train will replace the existing train on an 850km journey. If the bullet train does the journey 3hours faster than the existing train, what are their speeds?
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let V km/hr be the speed of the bullet train and so the speed of the
existing train is V - 40.
The time for the the bullet train to finish the whole journey is
850/V, while it takes 850/(V-40) hr for the existing train for the
journey. Since we know the time difference is 3 hrs, we have
3 + 850/V = 850/(V-40),
Cancel the denominator by multiply V(V-40):
3V(V-40) + 850(V-40) = 850 V,
Simplify: 3 V^2 - 120 V - 34000 = 0,

By quadratic formula,we get V = 20+ 200/3 SQRT(94) = 84.64 mile/hr
(the speed of the bullet train)
or 20 - 200/3 SQRT(94) [negative,invalid]
and so the speed of of the existing train is 44.64 miles/hr