# Fractions, Decimals & Percentages: Rational Number Word Problems (7th Grade Math)

I have a problem with one of the questions. The question was something like this:

Ashley takes 40 seconds to prepare one bag. She receives help from 4 friends in preparing bags. Each of her friends take 70 seconds to prepare one bag. How many hours will it take them all to prepare 1575 bags?

To answer this question, I used this method:

Step 1 – Find the lowest common multiple of 40 and 70, which is 280.

Step 2 – In 280 seconds, Ashley can prepare 7 bags, and each of her 4 friends can prepare 4 bags. That's 23 bags in total.

Step 3 – The average time taken between all 5 of them in preparing one bag is 280 ÷ 23 = 12.17391304 seconds

Step 4 – The total time taken in hours in preparing 1575 bags is 1575 x 12.17391304 ÷ 3600 = 5.326086957 hours

Khan Academy told me this was the wrong answer, and showed the apparently correct method of working out the answer:

Step 1 – Find the average time it takes one of them to prepare one bag: (40 + (4 x 70)) ÷ 5 = 64 seconds

Step 2 – Since there are 5 workers, it's 5 times faster, so 64 ÷ 5 = 12.8 seconds

Step 3 – The total time taken in hours in preparing 1575 bags is 1575 x 12.8 ÷ 3600 = 5.6 hours.

I later realised an alternative to my method:

Follow steps 1 and 2 of my method.

Step 3 – 1575 ÷ 23 = 68 with a remainder of 11, so 68 bouts, each lasting 280 seconds, produces 1564 bags.

Step 4 – the remaining 11 bags can be produced in 140 seconds. In this time, each of Ashley's 4 friends can prepare 2 bags, and Ashley can prepare 3 bags and finish 20 seconds before the others.

Step 5 – 68 bouts of 280 seconds is 19,040 seconds

Step 6 – 19,040 seconds plus the remaining 140 seconds is 19,180 seconds

Step 7 – 19,180 seconds ÷ 3600 = 5.327777778 hours

To me, the third method seems like it should produce the correct result, but Khan Academy had different ideas. And the first two methods seem to me like they should both produce the same result, but they don't. Can anyone explain this please?

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