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Three inlet pipes A, B, and C can fill a tank in 8 hours, 12 hours, and 24 hours, respectively. First, pipe A is opened alone for 1 hour. Then pipe B is opened, and both A and B run together for the next 2 hours. After that, pipe C is also opened, and all three pipes run together until the tank is full. How much total time, from the start, will it take to fill the tank?
4 hour 30 minutes
4 hour 40 minutes
4 hour 20 minutes
4 hour 50 minutes
4 hour 50 minutes
Use total units as the LCM of 8, 12, and 24, which is 24 units. Calculate hourly efficiencies as 3, 2, and 1 units/hr respectively and subtract work done step-by-step.
Inlet pipes A, B, and C fill a tank in 8, 12, and 24 hours respectively. Different sequences of activation are used to fill the tank.
Work=Efficiency├ЧTime
Use total units as the LCM of 8, 12, and 24, which is 24 units. Calculate hourly efficiencies as 3, 2, and 1 units/hr respectively and subtract work done step-by-step.
Students often forget to include the initial work done by A and (A+B) when calculating the remaining work for the final stage.
Calculate Efficiency
Find the LCM of 8, 12, and 24 to get total capacity: 24 units. Efficiencies are: A = 24/8=3 units/hr, B = 24/12=2 units/hr, C = 24/24=1 unit/hr.
EAтАЛ=3,EBтАЛ=2,ECтАЛ=1
Calculate work done in segments
Pipe A runs alone for 1 hour (3 units). Pipes A and B run together for 2 hours (2+3 = 5 units/hr ├Ч 2 hrs = 10 units). Total work done so far is 3+10=13 units.
WdoneтАЛ=3+(3+2)├Ч2=13
Calculate remaining work and time
Remaining work is 24тИТ13=11 units. All three pipes (A+B+C) work together with combined efficiency 3+2+1=6 units/hr. Time required = 11/6 hours.
T=611тАЛ=1┬аhr┬а50┬аmins
Calculate total time
Total time = 1 hr (A) + 2 hrs (A+B) + 1 hr 50 mins (A+B+C) = 4 hours 50 minutes.
TtotalтАЛ=1+2+165тАЛ=4┬аhrs┬а50┬аmins
D is correct because the sum of the time intervals leads to a total duration of 4 hours and 50 minutes.
This concept is fundamentally similar to 'Relative Speed' problems in Physics, where multiple agents contribute to a single net rate of change.
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