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Two pipes can fill a tank in 34 hours and 94 hours, respectively. The time (in hours) required to fill the tank when both pipes are opened simultaneously is:
30796тАЛ
29797тАЛ
32799тАЛ
31798тАЛ
32799тАЛ
Use the product divided by the sum formula for two pipes working together. Since 34├Ч94=3196 and 34+94=128, the time is 3196/128, which simplifies by dividing by 4 to 799/32.
Pipe A fills a tank in 34 hours, Pipe B fills a tank in 94 hours.
T=A+BA├ЧBтАЛ
Use the product divided by the sum formula for two pipes working together. Since 34├Ч94=3196 and 34+94=128, the time is 3196/128, which simplifies by dividing by 4 to 799/32.
Students often add the rates incorrectly or fail to simplify the resulting large fraction.
Define the work rates
Let the rate of Pipe A be 1/34 tanks per hour and the rate of Pipe B be 1/94 tanks per hour.
RatecombinedтАЛ=341тАЛ+941тАЛ
Calculate combined rate
Find the sum of the fractions. The denominator is 34├Ч94=3196 and the numerator is 94+34=128.
RatecombinedтАЛ=3196128тАЛ
Calculate total time
The time taken is the reciprocal of the combined rate.
Time=1283196тАЛ
Simplify the fraction
Divide both numerator and denominator by 4 to simplify the result.
Time=128├╖43196├╖4тАЛ=32799тАЛ
C is correct because the combined time required is 799/32 hours.
This concept is fundamentally identical to 'Combined Resistance' in Physics (1/RtтАЛ=1/R1тАЛ+1/R2тАЛ) or 'Combined Speed' in relative motion problems.
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