ExplanationSince Sabrina and Janis are working together, add their rates. Sabrina completes 1 tank in 8 hours, so she works at a rate of \(\frac{1}{8}\) tank per hour. Likewise, Janis works at a rate of \(\frac{1}{13}\) tank per hour. Now, add these fractions:
\(\frac{1}{8}+\frac{1}{13}=\frac{13}{104}+\frac{8}{104}=\frac{21}{104}\) tanks per hour, when working together.
Next, plug this combined rate into the W = RT formula to find the time. You might also notice that since the work is equal to 1, the time will just be the reciprocal of the rate:
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At this point, you do not need to do long division or break out the calculator! Just approximate: \(\frac{104}{21}\) is about 100 ÷ 20 = 5.
Alternatively, use some intuition to work the answer choices and avoid setting up this problem at all!
You can immediately eliminate (A) and (B), since these times exceed either worker’s individual time.
Also, since Sabrina is the faster worker, Janis’s contribution will be less than Sabrina’s. The two together won’t work twice as fast as Sabrina, but they will work more than twice as fast as Janis.
Therefore, the total time should be more than half of Sabrina’s individual time, and less than half of Janis’s individual time. 4 < t < 6.5, which leaves (D) as the only possible answer.
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