Question

An Express train takes 1 hours less than a passenger train to travel 132kms if the average speed of the Express train is 11km per hour more than that of the passengers train find the average speed of the two trains ​

Answer 1

Step-by-step explanation:

Let the time taken by the express train = x

The time taken by the passenger train= x-1

distance traveled = 132km

Speed = Distance÷Speed

therefore,

Speed of the express train= 132÷x

Speed of the passenger train = 132÷(x-1)

Speed of express train is 11km/h more than the speed of passenger train. so we add 11 to speed of the passenger train.

$\frac{132}{x} = \frac{132}{x - 1 } + 11$

$\frac{132}{x} - \frac{132}{x - 1} = 11$

$\frac{132x - 132 - 132x}{x {}^{2} - x } = 11$

$132 = 11(x {}^{2} - x)$

$132 = 11x {}^{2} - 11x$

$0 = 11x {}^{2} - 11x - 132$

on dividing the above equation by 11, we get

$x {}^{2} - x - 12 = 0$

on splitting the middle term of the above trinomial we get,

$x {}^{2} - 4x + 3x - 12 = 0$

we factorise the above expression

$x(x - 4) + 3(x - 4) = 0$

$(x - 4)(x + 3) = 0$

$x - 4 = 0 \\ x = 4$

similarly

$x + 3 = 0 \\ x = - 3$

since the time cannot be negative; therefore the value of x = 4;

x is the time taken by the express train. The speed of the express train = 132/4

Speed of express train= 33km/hr

Speed of the passenger train = 33-11

Speed of the passenger train = 22km/hr