Question

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

Answer 1

Answer:

The average speed of express train is 44 km/h .

Step-by-step explanation:

Given as :

The distance between Mysore and Bangalore = D = 132 km

The time taken by passenger train = T hours

The time taken by express train = T' = ( T - 1 ) hours

The average speed of passenger train = S km/h

The average speed of express train = S' = (S + 11 ) km/h

According to question

Distance = Speed × Time

For passenger train

D = S × T

Or, 132 = S × T                     .......1

Again

For express train

D = S' × T'

Or, 132 = (S +11) × (T - 1)

Or, 132 = S T - S + 11 T - 11

Or, 132 = 132 - S + 11 T - 11

Or, S - 11 T + 11 = 0

Put the value of T from eq 1

i,e S - 11 × $\dfrac{132}{S}$ + 11 = 0

Or, S² + 11 S - 1452 = 0

Or, S² + 44 S - 33 S - 1452 = 0

Or, S ( S + 44 ) - 33 ( S + 44 ) = 0

∴  ( S + 44 ) ( S - 33 ) = 0

i.e S = 33

So, The average speed of passenger train = S = 33 km/h

And The average speed of express train = S' = (33 + 11 ) = 44 km/h

Hence, The average speed of express train is 44 km/h . Answer