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Two pipes, A and B, can fill a tank of 1000 litres in 5 hours and 6 hours, respectively. If they are opened together, how many hours will they take to fill an empty tank of 1800 litres?
1154
1145
1125
1152
1154
Calculate individual rates (litres/hour): RA=1000/5=200, RB=1000/6=500/3. Combined rate R=200+166.67=1100/3 L/hr. Time T=1800/(1100/3)=5400/1100=54/11 hours.
Pipe A fills 1000 litres in 5 hours, Pipe B fills 1000 litres in 6 hours. Find time to fill 1800 litres together.
T=RA+RBW
Calculate individual rates (litres/hour): RA=1000/5=200, RB=1000/6=500/3. Combined rate R=200+166.67=1100/3 L/hr. Time T=1800/(1100/3)=5400/1100=54/11 hours.
Students often try to find the LCM of 5 and 6 (which is 30 hours for 1000 litres) and then scale, but the target volume (1800 litres) changes the context, making the rate method more direct.
Calculate individual rates
Pipe A fills 1000 litres in 5 hours, so its rate is RA=51000=200 litres/hour. Pipe B fills 1000 litres in 6 hours, so its rate is RB=61000=3500 litres/hour.
RA=200,RB=3500
Calculate combined rate
When opened together, their combined rate R is the sum of individual rates: R=200+3500=3600+500=31100 litres/hour.
R=31100
Calculate time for 1800 litres
To find the time T required to fill 1800 litres, divide total volume by combined rate: T=311001800=1800×11003=1118×3=1154 hours.
T=1154
A is correct because the calculated time to fill 1800 litres is 54/11 hours.
This is a standard 'Work, Time, and Rate' problem. Always convert capacity to 'units per hour' to handle different tank sizes efficiently.
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