The key idea
Turn times into rates: a job done in t hours means t1 of the job per hour. Rates working together add; a drain subtracts. Work done = rate × time.
The trap
Adding the times instead of the rates.
Can Desmos do it?
Desmos can solve a1+b1=t1 for you, but it can't tell you that rates, not times, are what add.
College Board skill: Ratios, rates, proportional relationships, and units · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
Pump A can fill a tank in 5 hours, and pump B can fill the same tank in 3 hours. Working together, how many hours do the two pumps take to fill the tank?
Show the answer
Answer: 15/8Pump A fills 51 of the tank per hour and pump B 31. Together: 51+31=158 per hour, so the job takes 815 hours.
Level 2 · Test level
Working together, Ana and Ben can paint a room in 6 hours. Working alone, Ana can paint the room in 15 hours. How many hours would Ben take to paint the room alone?
Show the answer
Answer: 10Together they paint 61 of the room per hour, and Ana paints 151. Ben's rate is the difference: 61−151=101, so Ben alone takes 10 hours.
Level 3 · Beyond the test
Pipe A alone can fill a tank in 5 hours. Pipe B alone can empty the full tank in 9 hours. The tank is 21 full when both pipes are opened at the same time. How many hours will it take to fill the tank?
Show the answer
Answer: 45/8The net rate is 51−91=454 of the tank per hour. The tank needs 21 more, which takes 21÷454=5.625 hours.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
Percent change, chained and reversedChained and reversed percent changes, and the right base.36 questions, 3 levelsRates and unit conversionConversion factors, compound units and square units.36 questions, 3 levelsMixtures and concentrationConcentration problems: mixing, adding water, draining and replacing.36 questions, 3 levelsMeans, medians, and changes to dataTotals, combined groups and the score you need next.36 questions, 3 levelsConditional probability“Given that” from tables and percents.36 questions, 3 levelsRatios and proportionsRatios that change when one part changes.36 questions, 3 levels