Sachin, Dravid and Ganguly are visiting the Dhoni’s family who are staying 400 km away. Each of their walking speeds is 20 kmph. Initially, Dravid and Ganguly travel in a car at the rate of 100 kmph and Sachin walks the distance. After a while, Ganguly gets off the car as he feels nauseated and walks the rest of the distance to the house. Dravid goes back in the car to fetch Sachin and they all reach the house at the same time. What was the entire time involved in travelling?
Answers
Given : Sachin, Dravid and Ganguly are visiting the Dhoni's family who are staying 400 km away. Each of their walking speeds is 20 kmph. Initially, Dravid and Ganguly travel in a car at the rate of 100 kmph and Sachin walks the distance. After a while, Ganguly gets off the car as he feels nauseated and walks the rest of the distance to the house. Dravid goes back in the car to fetch Sachin and they all reach the house at the same time
To find : What was the entire time involved in travelling?
Solution:
Let say after 100x km Dravid drop Gangualy
Time taken = 100x/100 = x hr
Remaining Distance = 400 - 100x km
Time taken by Ganguly further = (400 - 100x)/20 = 20 - 5x hr
Total time = x + 20 - 5x = 20 - 4x
now after x hrs
Sachin covered Distance = 20x
Distance between Sachin & Dravid = 100x - 20x = 80x
Time taken to cover 80x by Sachin & Dravid = 80x/(100 +20) hr
= 2x/3 hr
distance covered by sachin in 2x/3 hr = 40x/3 km
Remaining Distance = 400 - 20x - 40x/3 = 400 - 100x/3 km
Further time taken = (400 - 100x/3)/100 = 4 - x/3 hr
x + 2x/3 + 4 - x/3 = 20 - 4x
=> 5x + x/3 = 16
=> 16x/3 = 16
=> x = 3
20 - 4x = 20 - 4*3 = 8
Total time Taken = 8 hrs
ist after 3 hrs at distance of 300 km Ganguly dropped
and ganguly took further 5 hrs to cover remaining 100 km
in 3 hrs sachin covered 60 km
So distance between dravid & sachin = 300 - 60 = 240 km
in next 2 hrs Dravid goes back 200 km & sachin 40 km to meet each other
so they are 100 km from initial point
now next 300 km dravid & sachin covered in 3 hrs
3 + 2 + 3 = 8 hrs
entire time involved in travelling = 8 hrs
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