Question

An express train takes 2 hours less than a passenger train to travel 132 km between A and B. If the average speed of express is 10 km/hr more than that of passenger train, find the average speed of two trains.

Answer 1

Answer:

Suppose,

The speed of passenger train be x km/hr

Hence speed of express train = (x +10) km/hr

Given,

Distance travelled by both the trains = 132 km

Time taken by the passenger train = 132/x hrs

Time taken by the express train = 132/(x + 10) hrs

Time taken = (Distance)/(Speed)

$Hence,\frac{132}{x} - \frac{132}{x+10} = 2\\ => 132[\frac{x+10-x}{x(x+10)} ] = 2$

⇒132 × 10 = 2x^2 + 22x

⇒2x^2 + 22x – 1320 = 0

#ERROR IN QUESTION

#Correction : An express train takes 1 hour less than a passenger train to travel 132 km/hr between A and B .If the average speed of the express train is 11 km/hr more than that of passenger train, find the average speed of both trains.

Suppose,

The speed of passenger train be x km/hr

Hence speed of express train = (x +11) km/hr

Given ,

Distance traveled by both the trains = 132 km

Time taken by the passenger train = 132/x hrs

Time taken by the express train = 132/(x + 11) hrs

Time taken = (Distance)/(Speed)

$Hence,\frac{132}{x} - \frac{132}{x+11} = 1\\ => 132[\frac{x+11-x}{x(x+11)} ] = 1$

= 132 × 11 = x(x + 11)

=  $x^2+11x-1452 = 0</p><p>=$$x2+44x-33x-1452 = 0$

= x(x + 44) – 33(x + 44) = 0

= (x + 44)(x – 33) = 0

= (x + 44) = 0 or (x – 33) = 0

=>  x = –44 or x = 33

Since speed cannot be negative, x = 33

The speed of passenger train is 33 km/hr and speed of express train is 44 km/hr.

Answer 2

Answer:

The speed of the passenger train is 21.17 kmph and the speed of express train is 31.17 kmph

Step-by-step explanation:

Let the speed of passenger train be x

=> time taken by the passenger train to cover 132 km = 132/x

speed of the express = x + 10

=> time taken by the express train to cover 132 km = 132/(x+10)

From the given data

132/x - 132/(x+10) = 2

=> 132x + 1320 - 132x = 2x² + 20x

=> 2x² + 20x - 1320 = 0

=> x² + 10x -660 = 0

solving the quadratic equation we get,

x = 21.17 or -31.17

rejecting the -ve value we get

x = 21.17

hence average speed of passenger train = x = 21.17

average speed of express train = x + 10 = 21.17 + 10 = 31.17