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Question
The speed of an ordinary train is x km per hr and that of an express train is (x + 25) km per hr.
- Find the time taken by each train to cover 300 km.
- If the ordinary train takes 2 hrs more than the express train; calculate speed of the express train.
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Solution
i. Speed of ordinary train = x km/hr
Speed of express train = (x + 25) km/hr
Distance = 300 km
We know
`"Time" = "Distance"/"Speed"`
∴ Time taken by ordinary train to cover 300 km = `300/x` hrs
Time taken by express train to cover 300 km = `300/(x + 25)` hrs
ii. Given that the ordinary train takes 2 hours more than the express train to cover the distance.
Therefore,
`300/x - 300/(x + 25) = 2`
`(300x + 7500 - 300x)/(x(x + 25)) = 2`
`7500 = 2x^2 + 50x`
`2x^2 + 50x - 7500 = 0`
`x^2 + 25x - 3750 = 0`
`x^2 + 75x - 50x - 3750 = 0`
`x(x + 75) - 50(x + 75) = 0`
`(x + 75)(x - 50) = 0`
x = –75, 50
But, speed cannot be negative.
So, x = 50.
∴ Speed of the express train = (x + 25) km/hr = 75 km/hr.
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