Let the total fries in the plate are 30
Mary eats 2 fries per minutes
Ann eats 1 fries per minutes
so in 2 minutes they eat 3 fries.
To eat 30 fries they need 20 minutes
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Mary's rate 1/15
Ann's rate 1/30

so in 2 mins they both will eat 1/15+1/30 part of the french fries.
3/30 part of the french fries will be eaten in 2 mins, so in order to complete full plate of french fries, they will need 10 such cycles.
Therefore total time needed = 10*2 = 20 mins
Hence Answer is D.

Kudos if it helps.

Use 30 fries (or any reasonable multiple of 15 and 30) to find out how many fries per minute each person eats. 1 plate, P = 30 fries. Substitute 30 fries, F, for 1 plate, P.

Mary = \(\frac{1P}{15min}\) = \(\frac{30F}{15min}\). Reduce.

M's rate = \(\frac{2F}{1min}\)

A's rate: \(\frac{1}{30}\) = \(\frac{30F}{30min}\) = \(\frac{1F}{1min}\)

There are 30 fries. Mary eats two fries in one minute. Ann eats one fry in 1 minute. But they don't eat during the same minute.

First minute: Mary eats two fries

Next minute: Ann eats one fry

So after two minutes, they have eaten 3 fries. How long will it take them to eat 30 fries?

\(\frac{3F}{2 min} = \frac{30F}{X mins}\)

3x = 60
x = 20 minutes

Answer D
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Marty eats 1/15 of a plate in a minute
Ann eats 1/30 of a plate in a minute

1/15 + 1/30 + 1/15 + 1/30 + ......... = 1
1/15 + 1/30 = 1/10 in 2 minutes
10* 1/10 in 2 * 10 minutes
=20 minutes

IMO D
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