Question

A passenger train takes 1 hr more than an express train to travel a distance of 240 km from Chennai to Virudhachalam.

The speed of passenger train is less than that of an express train by 20 km per hour. find the average speed of both trains​

Answer 1

Given:

The distance is 240 km

Passenger train takes 1 hour more than the express train

Passenger train is 20 km/h slower than the express train

To Find:

Their average speed

Solution

Define x:

Let the time taken by the express train be x hour

The time taken by the passenger train (x + 1) hour

Find the speed taken for the express train:

Speed = Distance ÷ Time

Speed = 240/x km/h

Find the speed taken for the passenger train:

Speed = Distance ÷ Time

Speed = 240/(x + 1) km/h

Solve x:

Given that the passenger train is 20 km/h slower

240/x - 240/(x + 1) = 20

240/x - 240/(x + 1) = 20

240(x + 1) - 240x = 20x(x + 1)

240x + 240 - 240x = 20x² + 20x

20x² + 20x - 240 = 0

20(x - 3)(x + 4)  = 0

x = 3 or x = -4 (rejected, since time cannot be negative)

Find the time taken:

Express train = x hours

Express train = 3 hours

Passenger train = x + 1 hours

Passenger train = 3 + 1 hours

Passenger train = 4 hours

Find the average speed:

Average Speed = Total Distance ÷ Total Time

Average Speed = (2 x 240)  ÷ (3 + 4)

Average Speed = 480 ÷ 7

Average Speed = 68.57 km/h

Answer: The average speed of both the trains is 68.57 km/h

Answer 2

$\large\underline\mathrm{Solution}$

Let the time taken by the express train be x hours.

The time taken by the passenger train (x - 1) hours.

The speed taken for the express train.

$\implies$ speed = dist/time

$\implies$ 240/x

The speed taken for the passenger train.

$\implies$ speed = dist/time

$\implies$ 240/(x - 1)km/h

The passenger train is 20km/h.

$\implies$ 240/x = 240/(x -1) = 20

$\implies$ 240/(x -1) - 240x = 20x(x - 1)

$\implies$ 240x + 240 - 240x = 20x² + 20x

$\implies$ 20x² + 20x - 240 = 0

$\implies$ 20(x - 3) (x + 4) = 0

$\implies$ x = 3. or. x = -4.