Question

Mr. Williams can grade 50 essays in 7 hours. His assistant, Mr. Wilfred, can do the same job in 14 hours. His other assistant, Ms. Stealth, can grade 25 essays in 6 hours. How long will it take them to grade 200 essays if all three work together?

Answer 1

13.44 or 13 11/25 hours

Explanation:

First use this format: number of essays/hours

- they are asking if all three work together, how many hours would it take, so this means addition:

50/7 + 50/14 + 25/6 = 200/x

Second, solve:

- least common multiple: 42

300/42 + 150/42 + 175/6 = 200/x

625/42 = 200/x

- cross-multiply

625x = 8,400

x = 336/25 = 13 11/25 = 13.44 (any one of these answers would work)