Question

A train travels at a certain average speed of 54 km and then travels a distance of 63 km at an average speed of 6km/h more than its average speed. If it takes 3 hours to complete the journey, what is its original average speed?​

Answer 1

Answer:

36km/hr is the speed

Step-by-step explanation:

Solution :

Distance =54km

Let the average speed be x

Distance =63 km

The average speed to cover this distance =x+6

Total time taken =3hr

DS=t

∴54x+63x+6=3

54(x+6)+63xx(x+6)=3

54x+324+63x=3x2+18x

=> 3x2−99x−324=0

=> x2−33x−108=0

(x−36)(x+3)=0  

x=36 or −3

x=−3 is not admissible

Hence x=36km/hr is the speed

Answer 2

Answer:

Let the average speed of the train be x km/hr

Distance travelled by train =54 km

D=S x t

54=(x) t

T=54/x............(1)

Distance travelled by train =63km

New speed= (6+x)

D= S x T

63 = (6+x) t

T= 63/6+x.............(2)

According to question:-

54/x + 63/x+6=3

54x + 324 + 63x/ x^2 + 6x =3

54x+324+63x = 3x^2 +18x

3x^2 - 99x -324=0

Now solve it by middle term splitting