Question

A fast train takes 3 hour less than a slow train for a joirney of 600 km. If the speed of the slow train is 10 km per hour less than that of the fast train find the speed of two train.

Answer 1

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Solution:-
Let the speed of the slow train be 'x' km/hr and the speed of the fast train be (x+10) km/hr.
Time taken by the slow train to cover the distance of 600 km = (600/x) hours
Time taken by the fast train to cover the distance of 600 km = 600/(x+10) hours.
Now, according to the question.
(600/x) - 600/(x+10) = 3
{600(x+10) - 600x}/x(x+10) = 3
600x + 6000 - 600x = 3{x(x+10)}
6000 = 3x² + 30x
3x² + 30x - 6000 = 0 Dividing it by 3 we get
x² + 10x - 2000
x² + 50x - 40x - 2000 = 0
x(x+50) - 40(x+50) = 0
(x-40) (x+50)
x = 40 or x = -50
x = -5 is not possible, the speed cannot be in negative.
So, x = 40
Speed of the slow train is 40 km/hr and the speed of the fast train is 40 + 10 = 50 km/hr.
Answer. 

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Answer 2

Let the speed of fast train be xkm/hrs
then,
600 600
------- -- --------- =3
x-10 x

x-x+10 3
---------- = ----
x (x-10) 600

10 1
---- = ----
x2-10x 200

x2-10x-2000 =0
x2-50x+40x-2000 =0
x(x-50) +40 (x-50)=0
(x-50)(x+40)=0
therefore,
x=50 :x=-40
speed can't be negative
therefore

x=50km/hrs. answer.

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