X=v*t problem?

Question

a train usually goes 800 km in speed v.
one day,the train past 400km in 0.8v and another 400km in 1.2v
as a result of this it tooked the train 20 more minutes to do this.
what is the usual speed of the train?

Answer 1

Let D = v t
t = 800 / v is usual time for journey

t1 = 400 / (0.8 v)
t2 = 400 / (1.2 v)
20 mins = 1 / 3 hour

400 / (0.8 v) + 400 / (1.2 v) = 800 / v + 1 / 3
1200 + 800 = 1920 + 0.8 v
0.8 v = 80
v = 100

Usual speed of train = 100 km / h

Answer 2

t1=400/0.8v
t2= 400/1.2v
t==800/v
t1+t2=t+20 (in minutes)
so
500/v+333.33/v =800/v+20
33.33/v=20 so v= 1.67km/min=100km/h