maths

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the distance between two stations is 340 km two trains start simultaneously on parallel tracks to each other . the speed of one of them is greater than that of the other by 5 km/hr. if the distance between the two trains after 2 hrs of their start is 30 km , find the speed of each train

• maths - ,

Two trains with speeds s and s+5 km/hr.
Initial distance=340 km
final distance = 30 km
Total distance travelled = 340-30=310 km
Total speed = s+s+5=2s+5
Time = 2 hrs
Form equation equating distance travelled
Time*speed=distance, or
2(2s+5)=310
2s+5=155
2s=150
s=75
Speeds of trains are 75 km/h and 80 km/hr

• maths - ,

If one train has a velocity of V km/h, the other one will have velocity V+5 km/h approaching the first train. Therefore Relative velocity will be V+V+5=2V+5 km/h.
Distance travelled by them in 2 hrs is 340-30=310km which is =2(2V+5)
Thus 4V+10=310 or 4V=300 hence V=75km/h and other train has a velocity of 80km/h.
Check: in 2 hrs they will move 75x2+80x2=150+160=310km =340-30 km. OK.