SOLUTION: a train normally travels 240km at a certain speed. one day, due to bad weather, the train's speed is reduced by 20km/h so that the journey takes two hours longer. find the normal s

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Question 180852: a train normally travels 240km at a certain speed. one day, due to bad weather, the train's speed is reduced by 20km/h so that the journey takes two hours longer. find the normal speed.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
a train normally travels 240km at a certain speed. one day, due to bad weather, the train's speed is reduced by 20km/h so that the journey takes two hours longer. find the normal speed.
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t = time
r = rate
t = 240/r
t+2 = 240/(r-20)
Sub for t
(240/r) + 2 = 240/(r-20)
240 + 2r = 240r/(r-20)
(240+2r)*(r-20) = 240r
(r+120)*(r-20) = 120r

(r-60)*(r+40) = 0
r = 60, -40
Ignore the negative result.
r = 60 kph

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a train normally travels 240km at a certain speed. one day, due to bad weather, the train's speed is reduced by 20km/h so that the journey takes two hours longer. find the normal speed.
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Normal-travel DATA:
distance = 240 km ; rate = x km/h ; time = d/r = 240/x hrs
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Bad weather DATA:
distance = 240 km ; rate = (x-20) km/h ;time = 240/(x-20) hrs
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Bad time - normal time = 2 hrs
240/(x-20) - 240/x = 2
120/(x-20) - 120/x = 1
120x -120(x-20) = x(x-20)
20 = x^2 -20x
x^2 - 20x - 20 = 0
x = [20 +- sqrt(20^2 - 4*1*-20)]/2
x = [20 +- sqrt(480)]/2
x = [20 +- 4sqrt(30)]/2
x = 10 +- 2sqrt(30)
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Cheers,
Stan H.