Quadratic equations - problems

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The discussion focuses on solving a quadratic equation derived from a train traveling 480 km at a uniform speed. The problem states that if the speed were reduced by 8 km/h, the journey would take 3 hours longer. The user correctly sets up two equations: 480 = xt and 480 = (x-8)(t+3), but struggles to progress. The solution involves substituting t from the first equation into the second to create a single-variable quadratic equation in terms of speed, x.

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manogyana25
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Missing template due to originally being posted in non-homework forum
A train travels a distance of 480km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Represent this situation in the form of quadratic equation.

So I have been trying this but couldn't find it.
I have taken the speed as x.
And time, t
Distance =speed *time
Then
480=xt
480=(x-8)(t+3)
I couldn't go any further. And I'm not sure if this is right or not.
I just started learning quadratic equations. And I don't have any depth in the subject. Help me solve it in an easy way. Thank you!
 
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manogyana25 said:
I have taken the speed as x.
Generally, avoid using x for speed as it is more regularly used for distances.

Apart from that (and the fact your quantities are missing units), you are doing well. You have two equations and two unknowns. Solve for t in one of them (I suggest the first) and insert the result into the other.
 
I have no problem with using "x" for speed! And in problems like this distance is more often "s" or "d".
(Though, personally, I would have used "v".)

manogyana25 said:
A train travels a distance of 480km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Represent this situation in the form of quadratic equation.

So I have been trying this but couldn't find it.
I have taken the speed as x.
And time, t
It would be better to say that t is the time required to travel 480 km at the original speed. Just "t is time" is ambiguous. And it would be better to say "x is the speed in km per hour and t is in hours" but those are a bit picky!

Distance =speed *time
Then
480=xt
480=(x-8)(t+3)
I couldn't go any further. And I'm not sure if this is right or not.
I just started learning quadratic equations. And I don't have any depth in the subject. Help me solve it in an easy way. Thank you!
From 480= xt,, t= 480/x. Replace t in the second equation with that to get a single equation in x.
 

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