Hritik, Abhishek and John run a race starting from the same point. They run at the speeds of 200, 300 and 400 m/min respectively. Abhishek being faster than Hritik, starts 10 minutes after Hritik. John being fastest starts even later. Abhishek and John overtake Hritik at the same time, how many after Abhishek does John start?
Answers
Answer:
5 min
Step-by-step explanation:
Given that :-
Speed of Hritik : 200 m/s
Speed of Abhishek : 300 m/s
speed of John : 400 m/s
They run a race from the same initial point.
Abhishek starts 10 min after Hritik.
John starts after Abhishek (Time unknown).
Abhishek and john overtake Hritik at the same time.
To find :-
Time at which John started after Abhishek.
Solution :-
{Points :-
1. Distance from initial point at which Abhishek overtakes Hritik
2. Finding the distance at which John overtakes Hritik
3. Finding the distance at which John overtakes Abhishek
4. Time taken by them to reach the distance o 6000 m from the initial point
5. Comparing equations to find the time John started later than Abhishek
6. Verifying results
7. Final answer}
1. As given in question, Hritik starts 10 min earlier than Abhishek.
: In 10 min, Hritik will cover distance = 10 min * 200 m/min
= 2000 m
: Point at which Abhishek overtakes Hritik = LCM of 2000 and 300
= 6000 m
(At a distance of 6000 m from initial point, Abhishek overtakes Hritik.)
2. As given in question, John overtakes Hritik at the same point Abhishek overtakes Hritik
: 6000 m from initial point.
3. Because he is the fastest among them and when Abhishek overtakes Hritik, he also overtakes him (Hritik), so he also overtakes Abhishek at the same point.
: 6000 m from initial point.
4. Time taken by Hritik to cover 6000 m = 6000/200
= 30 min. --(i)
Time taken by Abhishek to cover 6000 m = 6000/300 + 10
(Because as given in question, he is starting 10 min after Hritik and we are comparing the time among them.)
= 20 + 10
= 30 min. --(ii)
(Indicating the same point of overtaking)
Time taken by John to cover 6000 m = 6000/400 + 10 + x
(Here, 10 min is because Abhishek started 10 min later than Hritik and 'x' is because John started (x) min later than Abhishek which we had to find.)
= 15 + 10 + x
= 25 + x
5. Comparing equations (i) and (ii) :-
: 30 = 30
: L.H.S. = R.H.S. (Indicating the same point of overtaking.)
Comparing equations (ii) and (iii) :-
: 25 + x = 30
: x = 30 - 25
: x = 5 min
Comparing equations (i) and (iii) :-
: 25 + x = 30
: 25 + 5 = 30 (Put x = 5)
: 30 = 30
: L.H.S. = R.H.S. (Indicating the same point of overtaking.)
6. Comparing equations (i), (ii) and (iii) :-
30 = 25 + x = 30
30 = 25 + 5 = 30
30 = 30 = 30
(As given in question and told above, they met at same point when John overtook Abhishek and Hritik.)
7. Hence, John started 5 min later than Abhishek (and 15 min later than Hritik).