Question

Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?

A table showing Rate in part per minute, Time in minutes, and Part of Potatoes Peeled. The first row shows Simon and has StartFraction 1 Over 30 EndFraction, t, and t times StartFraction 1 Over 30 EndFraction. The second row shows Sophie, and has StartFraction 1 Over 45 EndFraction, t, and t times StartFraction 1 Over 45 EndFraction.

15 minutes
18 minutes
GPT 3.5
Let x be the amount of time it takes for Sophie and Simon to peel the potatoes together.

Rate of Simon + Rate of Sophie = Rate of Simon and Sophie working together
1/30 + 1/45 = 1/x
(3 + 2)/90 = 1/x
5/90 = 1/x
1/18 = 1/x

Therefore, it will take Sophie and Simon 18 minutes to peel the potatoes together.

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