Question

A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km / hr less than that of the fast rain, find the speed of the two trains.

Answer 1

Speed = distance/time 

Let the speed of the faster train be ‘a’ km/hr. 

Speed of the slow train = a – 10 km/hr 

Also, fast train takes one hour less than a slow train for a journey of 200 km.

\(\Rightarrow \frac{200}{a-10}-\frac{200}{a}=1\)

⇒ 200a + 2000 – 200a = a² – 10a 

⇒ a² – 10a – 2000 = 0 

⇒ a² – 50a + 40a – 2000 = 0 

⇒ a(a – 50) + 40(a – 50) = 0 

⇒ (a + 40)(a – 50) = 0 

⇒ a = 50 km/hr 

Speed of the trains is 50 km/hr, 40 km/hr