Question

a train travels a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6km \h more than the first speed if it takes 3 hours to complete the total journey .find speed

Answer 1

Solution :

Distance =54km=54km

Let the average speed be x

Distance =63 km

The average speed to cover this distance =x+6=x+6

Total time taken =3hr=3hr

DSDS=t=t

∴54x+63x+6∴54x+63x+6=3=3

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

54x+324+63x=3x2+18x54x+324+63x=3x2+18x

=> 3x2−99x−324=03x2−99x−324=0

=> x2−33x−108=0x2−33x−108=0

(x−36)(x+3)=0(x−36)(x+3)=0

x=36or−3x=36or−3

x=−3x=−3 is not admissible

Hence x=36km

there for the speed is 36km/h