Un tren emplea cierto tiempo en recorrer 240 km. Si la velocidad hubiera sido 20 km por hora mas que la que llevaba hubiera tardado 2 horas menos en recorrer dicha distancia . ¿En que tiempo recorrio los 240 km ?

the train needs 8 hours to travel the 240km

Explanation:

This can be translated to:

"A train needs a given time to travel 240 km. If the velocity was 20km/h more than the one it had, it would taken 2 hours less in trave that distance.

How long it take to travel the 240km?"

The time needed to travel a distance is:

time = distance/velocity.

Then, we can call time = T, velocity = V and distance = 240km

T = 240km/V

and we also have that if the velocity was 20km/h bigger, the time would be 2 hours less:

T - 2h = 240km/(V + 20km/h)

So we have two equations and two variables, to solve it, we can isolave V in the first equation and then replace it in the second.

T = 240km/V

V = 240km/T

Now we replace it in the second one:

T - 2h = 240km/(240km/T+ 20km/h)

now we solve this for T.

(T - 2h)*(240km/T+ 20km/h) = 240km

240km - 480km*h/T + (20km/h)*T - 40km = 240km

- 480km*h/T + (20km/h)*T - 40km = 0

 480km*h/T = (20km/h)*T - 40km

480km*h = (20km/h)*T^2 - 40km*T

so now we have a quadratic equation:

(20km/h)*T^2 - 40km*T -  480km*h = 0

The solutions of this quadratic equations are:

Here we need to choose the positive value for T, because the time must be positive

T = (40 + 200)/40 = 240/40 = 8

So the train needs 8 hours to travel the 240km

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