A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. What is the speed of the train?

2 Answers
Sep 27, 2017

40 (km)/h

Explanation:

Total Distance S=480 km
Formula For Speed
"speed"="distance"/"time"
Hence "distance"="speed"xx"time"

Case-I
let the uniform speed of Train =v (km)/h
and the time taken to complete distance =(t ) "hour"
Distance S="speed"xx"time"=vt . . . . . (equation 1)

Case-II
If speed has been 8km/h less then train would have taken 3 hours more to cover the same distance.
Now in this situation
speed of train =(v-8) (km)/h
and Time taken to complete distance =(t+3) hour
Distance S="speed"xx"time"=(v-8)(t+3) . . . . . (equation 2)

Since Distance for both cases are same .
Comparing equation 1 and equation 2, we get
=>vt=(v-8)(t+3)
=>vt=(v)(t+3)-8(t+3)=vt+3v-8t-24
cancel vt from both side
=>0=3v-8t-24
=>3v-8t=24
=>3v=24+8t
=>v=(24+8t)/3

but from equation 1 the value of t=S/v=480/v (hour)

=>3v=24+8(480/v)
=>3v^2=24v+3840
=>3v^2-24v-3840=0
=>v^2-8v-1280=0
factorize the quadratic equation
=>(v-40)(v+32)=0

v is either 40 (km)/h or -32 (km)/h

Speed is Positive hence
"Speed"=40 (km)/h

Sep 27, 2017

40 km/h

Explanation:

Suppose the speed of the train is x km/h.
It takes 480/x hours to travel, but if the speed were
8 km/h slower, it would take 480/(x-8) hours.

Now we've got the equation:
480/(x-8) = 480/x +3
This can be solved as follows.

  1. Multiple both sides of the equation by x(x-8).
    480x = 480(x-8) +3x(x-8)
  2. Deform and factorize the equation to solve it.
    x^2-8x-1280=0
    (x-40)(x+32)=0
    x=40, -32

Don't forget that the answer must be positive, so the speed
is x=40 km/h.

Let's check.
If we travel at 40 km/h, it takes 12 hours.
If we traveled at 32 km/h, it would take 15 hours, so the difference
is three hours and we've got the correct answer.