At a pottery unit, 3 men or 5 women can glaze a batch of pots in 20 hours. How long will 6 men and 5 women take together?

6\frac{2}{3}

hoursCorrect answerYour answer10 hoursCorrect answerYour answer15 hoursCorrect answerYour answer30 hoursCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

6 men are twice 3 men, so 6 men alone take 10 hours: rate $\frac{1}{10}$ .
5 women alone take 20 hours: rate $\frac{1}{20}$ .
Together: $\frac{1}{10} + \frac{1}{20} = \frac{3}{20}$ , so time = $\frac{20}{3} = 6\frac{2}{3}$ hours.

Worth noting

Averaging 10 and 20 hours gives 15 hours and adding them gives 30 hours — both slower than the men alone, which is impossible when helpers are added.

Ten questions from Time & Work, at your own pace.

Explanation