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Algebra1: Problems on Time and Distance
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Quadratic Equations

Problems on Time and Distance

Formulae to be used: Speed = Distance / Time, Time = Distance / Speed
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Example: A train travels a distance of 400 km at constant speed. If the speed of the train is increased by 5 km an hour, the Journey would have taken 2 hours less. Find the original speed of the train..
Solution: Let x km/hr be the constant speed of the train.
Then, time taken to cover 400 km = (400 / x) hrs
Time taken to cover 400 km when the speed is increased by 5 km/hr = 400 / (x + 5) hours.
It is given that the time to cover 400 km is reduced by 2 hours.
400 / x - 400 / (x + 5) = 2
400 (x + 5) - 400x / x(x+ 5)
(400x + 2000 - 400x)/ (x2 + 5x) = 2
= 2x2 + 10x = 2000
=> x2 + 5x - 1000 = 0
=> x2 + 30x - 25x - 1000 = 0
=> x2 + 5x - 1000 = 0
x = -34.2 or 29.2
But, x cannot be negative. Therefore, x = 29.2.
Hence, the original speed of the train is 29.2 km/hr.
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