Question

A train travels 40 km at a uniform speed of 30 km/h. Its average speed after travelling
40 km is 45 km/h for the whole journey. What will be speed in the second half of the journey?

Answer 1

@
ATQ
45km/h=40+40/ 40/30+40/x
45=80/4/3+40/x
45=80/4x+120/3x
45=80×3x/4x+120
45=240x/4x+120
45(4x+120)=240x
180x+5400=240x
5400=240x-180x
5400=60x
5400/60=x
90=x
speed for next half of journey =90km/h
@:-)

Answer 2

Given:
Total distance =80km
Average speed of entire journey=45km/h
Total Time taken =total distance/average speed
=80/45 hour
Case :1
Let us CALCULATE time taken to cover first 40km
Speed=30km/h
Distance=40km
T=distance/ speed=40/30
=4/3 hr -----equation ( 1)
Case: 2
Let us CALCULATE time taken to travel next 40km
Let speed be =Xkm/ h
X=40KM/t
t=40/X hours ----equation( 2)
Total time = add equation 1 and 2
=4/3 +40/x
Since total time =80/45 hr
80/45=4/3+40/x
80/45=4x+120/3x
3x(80)=45(4x+120)
80x=15(4x+120)
80x=60x+15*120
20x=15*120
x=15*120/20
X=90km/hr
Therefore bus should travel next 40km distance at a speed of 90 km/h