If a train runs with the speed of 48 km/h, it reaches its destination late by 12 minutes. However, if its speed is 64 km/h it is late by 3 minutes only. The right time to cover its journey (in minutes) is?
Question
If a train runs with the speed of 48 km/h, it reaches its destination late by 12 minutes. However, if its speed is 64 km/h it is late by 3 minutes only. The right time to cover its journey (in minutes) is?
Solution
To solve this problem, we need to set up two equations based on the information given.
Let's denote:
- D as the distance the train needs to travel
- T as the right time to cover its journey (in minutes)
- S1 as the slower speed (48 km/h)
- S2 as the faster speed (64 km/h)
We know that distance equals speed times time, so we can set up the following two equations:
- D = S1 * (T + 12/60)
- D = S2 * (T + 3/60)
We can convert the speeds from km/h to km/min by dividing by 60:
S1 = 48/60 = 0.8 km/min S2 = 64/60 = 1.0667 km/min
Substituting these values into the equations gives us:
- D = 0.8 * (T + 12/60)
- D = 1.0667 * (T + 3/60)
Since both equations equal D, we can set them equal to each other and solve for T:
0.8 * (T + 12/60) = 1.0667 * (T + 3/60)
Solving this equation gives us T = 57 minutes. So, the right time to cover the journey is 57 minutes.
Similar Questions
If a train runs at 40 km/h, it reaches its destination late by 11 min, but if it runs at 50 km/h, it is late by 5 min only. The correct time for the train to complete its journey is
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