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Questions
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.
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Solution
Let the original speed of train be x km/hr. Then,
Increased speed of the train = (x + 5)km/hr
Time taken by the train under usual speed to cover 360 km = `360/x`hr
Time taken by the train under increased speed to cover 360 km = `360/(x+5)`hr
Therefore,
`360/x-360/(x+5)=1`
`(360(x+5)-360x)/(x(x+5))=1`
`(360x+1800-360x)/(x^2+5x)=1`
`1800/(x^2+5x)=1`
1800 = x2 + 5x
x2 + 5x - 1800 = 0
x2 - 40x + 45x - 1800 = 0
x(x - 40) + 45(x - 40) = 0
(x - 40)(x + 45) = 0
So, either
x - 40 = 0
x = 40
Or
x + 45 = 0
x = -45
But, the speed of the train can never be negative.
Hence, the original speed of train is x = 40 km/hr
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