Quadratic equations - problems

Click For Summary
A train covers 480 km at a uniform speed, and if its speed were reduced by 8 km/h, it would take 3 hours longer to travel the same distance. The problem can be represented with two equations: 480 = xt and 480 = (x-8)(t+3). To solve for the speed, t can be expressed as 480/x and substituted into the second equation, yielding a single equation in x. This approach allows for the formulation of a quadratic equation to find the train's speed. Understanding the relationship between distance, speed, and time is crucial for solving such problems.
manogyana25
Messages
6
Reaction score
2
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!
 
Physics news on Phys.org
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.
 

Similar threads

Conceptual question on equations of the form ##x=ay^2+by+c##
  • · Replies 5 ·
Replies
5
Views
2K
Find the value of ##r## and ##s## in the given quadratic equation
  • · Replies 1 ·
Replies
1
Views
2K
Solving system of 3 quadratic equations
  • · Replies 4 ·
Replies
4
Views
2K
Value of "a" between two real roots of quadratic equation
  • · Replies 2 ·
Replies
2
Views
2K
Solve the quadratic equation that involves sum and product
  • · Replies 1 ·
Replies
1
Views
2K
Quadratic equation with no rational roots
  • · Replies 12 ·
Replies
12
Views
3K
Find integer points on this equation
  • · Replies 8 ·
Replies
8
Views
2K
Grade 11 Math Help Quadratic functions/ physics
  • · Replies 18 ·
Replies
18
Views
2K
Quadratic equation and its roots
  • · Replies 14 ·
Replies
14
Views
2K
Quadratic function minimal value
  • · Replies 11 ·
Replies
11
Views
2K