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Pipe A can fill a tank in 10 hours and Pipe B can empty it in 15 hours. If both are opened together, how long will it take to fill the tank?
25 hours
30 hours
20 hours
35 hours
30 hours
Use the product/difference rule: (Product of times) / (Difference of times). Here: (10 * 15) / (15 - 10) = 150 / 5 = 30.
Pipe A fills in 10 hours and Pipe B empties in 15 hours.
T=yтИТxxyтАЛ
Use the product/difference rule: (Product of times) / (Difference of times). Here: (10 * 15) / (15 - 10) = 150 / 5 = 30.
Students often incorrectly calculate the rate as (1/10 + 1/15) instead of subtracting the emptying pipe (1/10 - 1/15), treating both as filling pipes.
Calculate LCM of work
Assume the total capacity of the tank is the LCM of 10 and 15, which is 30 units.
LCM(10,15)=30
Determine efficiency
Rate of Pipe A is 30/10 = 3 units/hr (fill). Rate of Pipe B is 30/15 = 2 units/hr (empty). Combined efficiency is 3 - 2 = 1 unit/hr.
3тИТ2=1┬аunit/hr
Calculate final time
Divide total units by combined efficiency to get total time.
T=130тАЛ=30┬аhours
B is correct because the net rate of filling is 1 unit/hr, so 30 units take 30 hours to fill.
This concept of relative rates (filling vs emptying) is identical to relative speed in time, speed, and distance problems where two objects move in opposite directions.
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