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Answer :
Sure, let's solve this question step-by-step.
1. Initial conditions:
- We need to fill the first tank to a height of 80 cm.
- The rate of filling is 20 liters per minute.
- The time taken is 1 hour and 20 minutes.
2. Convert time into minutes:
- 1 hour = 60 minutes
- Additional time = 20 minutes
- Total time = 60 minutes + 20 minutes = 80 minutes
3. Calculate the total volume of water:
- Volume = fill rate × time
- Volume = 20 liters/minute × 80 minutes
- Volume = 1600 liters
4. New conditions to solve:
- We need to fill the second tank to a height of 90 cm with a filling rate of 30 liters per minute.
5. Comparing the heights:
- To find out how much more we need to fill compared to the initial tank height of 80 cm:
- Ratio of final height to initial height = 90 cm / 80 cm = 1.125
6. Calculate the new total volume needed:
- Final volume = Initial volume × (New height / Initial height)
- Final volume = 1600 liters × 1.125
- Final volume = 1800 liters
7. Calculate the time needed to fill to the new height at the new rate:
- Time = Final volume / New fill rate
- Time = 1800 liters / 30 liters per minute
- Time = 60 minutes
Summarizing:
- The initial conditions required 80 minutes to fill a tank with 1600 liters.
- To fill another tank to a height of 90 cm, it would need a total of 1800 liters.
- At a rate of 30 liters per minute, it would take 60 minutes to fill the second tank.
Therefore, it will take 60 minutes (1 hour) to fill the second tank to a height of 90 cm with a filling rate of 30 liters per minute.
1. Initial conditions:
- We need to fill the first tank to a height of 80 cm.
- The rate of filling is 20 liters per minute.
- The time taken is 1 hour and 20 minutes.
2. Convert time into minutes:
- 1 hour = 60 minutes
- Additional time = 20 minutes
- Total time = 60 minutes + 20 minutes = 80 minutes
3. Calculate the total volume of water:
- Volume = fill rate × time
- Volume = 20 liters/minute × 80 minutes
- Volume = 1600 liters
4. New conditions to solve:
- We need to fill the second tank to a height of 90 cm with a filling rate of 30 liters per minute.
5. Comparing the heights:
- To find out how much more we need to fill compared to the initial tank height of 80 cm:
- Ratio of final height to initial height = 90 cm / 80 cm = 1.125
6. Calculate the new total volume needed:
- Final volume = Initial volume × (New height / Initial height)
- Final volume = 1600 liters × 1.125
- Final volume = 1800 liters
7. Calculate the time needed to fill to the new height at the new rate:
- Time = Final volume / New fill rate
- Time = 1800 liters / 30 liters per minute
- Time = 60 minutes
Summarizing:
- The initial conditions required 80 minutes to fill a tank with 1600 liters.
- To fill another tank to a height of 90 cm, it would need a total of 1800 liters.
- At a rate of 30 liters per minute, it would take 60 minutes to fill the second tank.
Therefore, it will take 60 minutes (1 hour) to fill the second tank to a height of 90 cm with a filling rate of 30 liters per minute.
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