The distance between Delhi and Jaipur is 200 km. A train travells the first 100 km at the speed of 50km/hr. How fast much the train travells the next 100 km, so as to have average speed of 60 km/hr for the whole journey.
Answers
Given that, the distance between Delhi and Jaipur is 200 km.
Case 1)
A train travells the first 100 km at the speed of 50km/hr.
Distance = 100 km and speed = 50 km/hr
Time = Distance/Speed
t1 = 100/50
t1 = 2 hr
Case 2)
The train travells the next 100 km.
Let us assume that the train is traveling with a speed of 'x' km/hr.
t2 = 100/x
We have to find the speed of the train if the average speed of 60 km/hr for the whole journey.
Average speed = (Total distance covered)/(Total time taken)
According to question,
→ 60 = 200/(t1 + t2)
→ 60 = 200/(2 + 100/x)
→ 3 = 10/[(2x + 100)/x]
→ 3 = 10x/(2x + 100)
Cross-multiply them,
→ 3(2x + 100) = 10x
→ 6x + 300 = 10x
→ 6x - 10x = -300
→ -4x = -300
→ 4x = 300
Divide by 4 on both sides,
→ 4x/4 = 300/4
→ x = 75
Therefore, the speed of the train during the second part of the journey is 75 km/hr.