Question

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

Answer 1

Answer: 70 km/h

Explanation:

Let speed of passenger train = x ; and speed of express train = y

From the first statement,

Time taken by passenger train = Time taken by express train + 1 h

$\frac{240}{x}=\frac{240}{y}+1$

$\Rightarrow \frac{240}{x}-\frac{240}{y}=1$

$\Rightarrow \frac{1}{x}-\frac{1}{y}=\frac{1}{240}$

$\Rightarrow \frac{y-x}{xy} = \frac{1}{240}$

$\Rightarrow y-x = \frac{xy}{240}$

From the second statement,

Speed of passenger train = Speed of express train - 20 km/h

x = y - 20 ⇒ y - x = 20

From the 2 equations,

$\frac{xy}{240} = 20$

$\Rightarrow xy = 20\times240 = 4800$

Taking the second equation,

y - x = 20

⇒ (y - x)² = 20²

⇒ y² + x² - 2xy = 400

⇒ y² + x² - 2xy + 4xy = 400 + 4×4800      ;(xy = 4800)

⇒ y² + x² + 2xy = 400 + 19200

⇒ (x + y)² = 19600

⇒ x + y = 140

⇒ (x + y)/2 = 140/2 = 70

⇒ Average speed of two trains = 70 km/h

Hope it helped :)