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Question
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
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Solution
Let the speed of the fast train be x km/hr.
The speed of the slow train is (x − 10) km/hr.
Using the formula:
Time = `"Distance"/"Speed"`
Time taken by the fast train to cover 200 km (T1) = `200/xhr`
Time taken by the slow train to cover 200 km (T2) =`200/(x-10)hr`
∴ `200/(x - 10) - 200/x = 1`
`rArr (200x - 200(x - 10))/(x(x - 10)) = 1`
`rArr (200x - 200x + 2000)/(x^2-10x) = 1`
`rArr 2000/(x^2 - 10x) = 1`
⇒ 2000 = x2 − 10x
⇒ x2 − 10x − 2000 = 0
⇒ x2 − 50x + 40x − 2000 = 0
⇒ x(x − 50) + 40(x − 50) = 0
⇒ (x − 50)(x + 40) = 0
x − 50 = 0 or x + 40 = 0
x = 50 or x = −40
But, the speed of the train can never be negative.
Thus, when x = 50
The speed of the slow train is x − 10 = 50 − 10
= 40
Hence, the speed of the fast train is x = 50 km/hr
The speed of the slow train is x = 40 km/hr respectively.
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