A passenger train takes 1 hr more than an express train to travel a di

1.	A passenger train takes 1 hr more than an express train to travel a distance of 240 km from Chennai to Viruthachalam. The speed of passenger train is less than that of an express train by 20 km per hour. Find the average speed of both the trains.
Answer» Let speed of express train be x km per hour. \(\therefore\) speed of passenger train = (x - 20)km/h Total travelled distance = 240 km \(\therefore\) Time taken by express train is T₁ = \(\frac{Total\, Travelled\, distance}{speed\, of\, express\, train}\) = 240/x hour Time taken by passenger train is T₂ = \(\frac{240}{x-20}\) hour Since, given that T₂ - T₁ = 1 hour ⇒ \(\frac{240}{x-20}-\frac{240}x=1\) ⇒ 240\((\frac1{x-20}-\frac1x)=1\) ⇒ \(\frac{x-(x-20)}{x(x-20)}=\frac1{240}\) ⇒ \(\frac{20}{x(x-20)}=\frac1{240}\) ⇒ \(\frac1{x(x-20)}=\frac1{4800}=\frac1{80\times60}\) ⇒ \(\frac1{x(x-20)}=\frac1{80(80-60)}\) \(\therefore\) x = 80 Hence, speed of express train is 80km/hr and speed of passenger train is 60km/hr.

A passenger train takes 1 hr more than an express train to travel a distance of 240 km from Chennai to Viruthachalam. The speed of passenger train is less than that of an express train by 20 km per hour. Find the average speed of both the trains.

Answer»

Let speed of express train be x km per hour.

\(\therefore\) speed of passenger train = (x - 20)km/h

Total travelled distance = 240 km

\(\therefore\) Time taken by express train is

T₁ = \(\frac{Total\, Travelled\, distance}{speed\, of\, express\, train}\) = 240/x hour

Time taken by passenger train is

T₂ = \(\frac{240}{x-20}\) hour

Since, given that T₂ - T₁ = 1 hour

⇒ \(\frac{240}{x-20}-\frac{240}x=1\)

⇒ 240\((\frac1{x-20}-\frac1x)=1\)

⇒ \(\frac{x-(x-20)}{x(x-20)}=\frac1{240}\)

⇒ \(\frac{20}{x(x-20)}=\frac1{240}\)

⇒ \(\frac1{x(x-20)}=\frac1{4800}=\frac1{80\times60}\)

⇒ \(\frac1{x(x-20)}=\frac1{80(80-60)}\)

\(\therefore\) x = 80

Hence, speed of express train is 80km/hr and speed of passenger train is 60km/hr.