Question

on the 100 m track , a train travels  the first 30 km at the uniform  speed of 30 km/h. how fast must the train travel the next 70 km so as to average 40km/h for the entire trip?

 

 

Answer 1

Solution :-

Given : 

Distance 1 = 30 km

Distance 2 = 70 km

We know that speed = distance/time

and, Average speed = total distance/total time taken

When the train acquired a speed of 30 km/hr, the time taken = 30/30 = 1 hour

Average speed = 9distance 1 + distance 2)/(time 1 + time 2)

AS time 2 or t2 is time taken for the second part of the journey of 70 km 

⇒ 40 = 100/(1 + t2)

⇒ 40 + 40t2 = 100

⇒ 40t2 = 100 - 40

⇒ 40t2 = 60

⇒ t2 = 60/40

⇒ t2 = 1.5 

So, t2 or time taken to travel the second part of the journey is 1.5 hours.

Speed of the second part of the journey = distance 2/time 2

⇒ 70/1.5

⇒ 46.666 km/hr or 46.7 km/hr

Answer.

Answer 2

Given:
Let T be the time taken for the entire journey.
Total DISTANCE = 100m
Average speed for entire journey =40km/ h
As we know:
Average speed= TOTAL DISTANCE/
TOTAL time
Total time =100/40=10/4 hours

Time taken to cover first part of journey be t1.
Distance covered is 30km .
Average speed to cover 30km is 30km/ h
Time taken to cover part of journey: t1
t1= 30km/ 30km/ h
=1 hr
Time taken to cover second part of journey be t2
Distance covered is 70km
Let x be the average speed for covering 70km
Time t2=70/X
Total time= T=t1 + t2
=1+70/x
Total time is 10/ 4 hrs
So,
10/4 =70/x + 1
10/4=(70+ x)/x
5/2=(70+x)/x
5x =2 (70+x)
5x=140+2x
5x-2x=140
3x=140
X=140/3
=46.66km/ h
Therefore Train must travel at a average speed of 46.66 km/ h to cover 70km.