To solve this problem, we use the relationship between speed and time when distance is constant.
1. Finding the Speed of the Train
Let the original speed be v. After the accident, the speed becomes 43v.
When speed becomes 43 of the original, the time taken for the same distance becomes 34 of the original time.
The difference in time is caused by the 25 km stretch where the train would have traveled at its original speed instead of the reduced speed.
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In the second scenario, the train is "10 minutes sooner" than the first scenario. This means the 10 minute delay is saved over that 25 km distance.
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Let t be the time taken to cover 25 km at original speed v.
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The time taken at reduced speed is 34t.
The time saved is:
Now, calculate the original speed (v):
v=TimeDistance=0.5 hours25 km=50 km/hr
2. Finding the Total Distance
Let the total distance be D. The accident happened after 60 km. The remaining distance is (D−60) km.
For the remaining distance (D−60), the time delay is 40 minutes.
Using the same logic:
31×(Time to cover D−60 at speed v)=40 minutes
Time to cover (D−60)=120 minutes=2 hours
Now, find the distance (D−60):
D−60=Speed×Time=50 km/hr×2 hours=100 km
Final Answer:
The speed of the train is 50 km/hr and the total distance is 160 km.
Correct Option:
(c) 50 km/hr,160 km
