Question

A train travels a distance of 480km at a uniform speed. If the speed has been 8km/hr less it would have taken 3 hours more to cover the same distance. Find the speed of the train. ​

Answer 1

Step-by-step explanation:

A train travels a distance of 480km

480/v hour= 480/(v-8)-3

480/v=(480–3v+24)/(v-8)

480*(v-8)=480v-3v^2+24v

3v^2–24v-480*8

3v^2– 24v-3840

v^2–8v-1280

v^2–40v+32v-1280

v(v-40) +32(v-40)

(v-40)(v+32)= 0

v= 40 km/hour.

Answer 2

Step-by-step explanation:

Let the uniform speed be "X".

Distance travelled = 480 km.

Time taken = (480/X )hr.

So, according to question,

Speed = X-8

Time taken = {(480/X) - 3 }hrs

Distance = 480 km.

$distance1 = distance2 \\ \\ \frac{480}{x} \times x = (x - 8)( \frac{480}{x} - 3) \\ \\ 480 = 480 - 3x - \frac{3840}{x} + 24 \\ \\ 0 = \frac{ - 3 {x}^{2} - 3840 + 24x }{x} \\ \\ 3 {x}^{2} - 24x + 3840 = 0 \\ \\ {x}^{2} - 8x + 1280 = 0 \\ \\ {x}^{2} - 40x + 32x + 1280 = 0 \\ \\ x(x - 40) + 32(x - 40) = 0 \\ \\ (x + 32)(x - 40) = 0 \\ \\ so.......x = 40 \: km {hr}^{ - 1} \: as \: speed \: is \: always \: positive$