On a 100km track, a train travels the first 30 km at a uniform speed of 30km/h. How fast must the train travel the next 70 km so as to average 40 km/h for the entire trip?
Answers
Let the speed of the train of the next 70 km be X km/hr.
So, (30+X)/2= 40
Or,30+X = 80
Or, X=50
The train must travel the next 70 km at 50 km/hr for the next 70 km/hr.
The displacement of an object is the product of speed and time.
1st Distance D1 = 30 km
2nd Distance D2 = 70 km
The time taken to travel 30 km (D1) is 30 km/hr.
The average speed to travel the whole 100 km is average 40km/hr.
Average speed = (Distance 1+Distance 2)/(Time 1+ Time 2)
40 = 100/(1+Time 2)
40( 1 + time 2) = 100
40 + 40 T2 = 100
40 T2 = 100 - 40
40 T2 = 60
T2 = 60 / 40 = 1.5 km/hr
Speed for 70 km = Distance 2 /Time 2
Speed = 70/1.5 = 46.6
Speed for 70 km is 46.6 km/hr