Question

The distance from Mumbai to Pune is 192 km.An express train takes 2 hours less than a passenger train to reach a destination.Average speed of the Express train is 16km/h more than the average speed of the passenger train.Find the average speed of both the trains.

Answer 1

Let the average speed of the passenger train be x.
speed =distance/time
time=distance/speed
distance=192km.
time=192/x [for passenger train].
time=192/x+16 [for express train]
192/x-192/x+16=2
192x-192x +3072=2[x²+16x]
3072/2=x²+16x
1536=x²+16x
x²+16x-1536=0
[x-48] [x+32]=0
Therefore, x=48,-32.
Speed cannot be negative.
Therefore, the average speed of the passenger train is 48km/h,
the average speed of the express train is x+16=48+16=64km/h.

Answer 2

let speed of passenger train be x therefore
192/x-192/x+16=2
by solving this we get $x^{2}$+15x-1536=0
(x-32)(x+48)=0
x=32,-48
since speed cant be negative ,speed of passenger train is 32 km/h
and speed of express is 48 km/h