Question

In the quadratic problem: A train travels 300km at a uniform speed. If the speed had been 5km an hour more, the journey would have taken 2 hours less. Find the speed of the train?
Here the equation is set as 300/x - 300/x+5 = 2
what I would like to know is why I cant set the equation as 300/x+5 - 300/x = 2?
Is there any way to understand this rule?

Answer 1

No rule it is simple you see the first time let us assume as t₁ and the second time as t₂ 

now you see t₁ = 300/x and  t₂ = 300/(x+5)

here you see the denominator of t₂ is greater than that of t₁ so from here we can understand logically that t₁ is greater that that of t₂ since they have equal numerator 

Let me make u understand with a simple example let x₁ = 300/y  and x₂ = 300/(y + 5)

Let  y = 10 

so we get x₁ = 30 and x₂ = 20 you see x₁ > x₂ 

so now let us return to the problem ,you see in the same sense we get t₁ > t₂

so we always subtract smaller from greater number to get a positive result 

so thats why we here also do   t₁ - t₂     to get '+'tive 2  

Answer 2

Let x be the speed of train in kph
so at speed x kph it takes 300/x hrs to complete journey
At higher speed  x+5 it would take less time and complete journey in 300/(x+5) hrs
   We know 300/(x+5) is less than 300/x by 2 hrs
   That gives 300/x- 300/(x+5)=2