Question

a journey of 192 km takes 2 hours less by a fast train than by a slow train. if the average speed of the slow train be 16 kmph less than that of fast train, what is the average speed of the faster train? * 1 point 32 kmph 16 kmph 12 kmph 48 kmph

Answer 1

48 kmph.

Step-by-step explanation:

Let v be the speed of the slow train.

Then v + 16 is the speed of the fast train.

Let t be the time, the fast train travels 192 km.

Then t + 2 is the time, the slow train travels 192 km.

S = v × t

We can create a pair of simultaneous equations:

t(v + 16) = 192. vt + 16t = 192

v(t + 2) = 192. vt + 2v = 192

Therefore: 2v = 16t

. v = 8t

Substituting v in the previous equation, we get:

8t(t + 2) = 192

8t² + 16t - 192 = 0

t² + 2t - 24 = 0

(t + 6)(t - 4) = 0

As a negative value is not acceptable for the time, 4 is the answer. t = 4

So v = 8 × 4 = 32

And v + 16 = 48

So the speed of the faster train is 48 kmph.