Example 16 : On a 100 km track, a train travels first 30 km at a unifo

1.	Example 16 : On a 100 km track, a train travels first 30 km at a uniform speed of30 km/h. How fast must the train travel the next 70 km so as its average speed is40 km/h for the entire trip?(CBSE 2011)
Answer» 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 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.

Example 16 : On a 100 km track, a train travels first 30 km at a uniform speed of30 km/h. How fast must the train travel the next 70 km so as its average speed is40 km/h for the entire trip?(CBSE 2011)

Answer»

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

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.