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eating potatoes

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by hk » Fri Jun 12, 2009 7:06 pm
Robert can eat a 20 kg bag of potatoes in 10 days. If together with his wife, Jane, they can eat the same bag in 7 days, how many days does it take Jane to eat a 20 kg bag of potatoes by herself?

1. 46 2/3
2. 23 1/3
3. 17
4. 12
5. 11 2/3
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by ssmiles08 » Fri Jun 12, 2009 7:16 pm
IMO B.

If Rob can eat 20 kg in 10 days, he can eat 2kg in 1 day (20/10)

in 7 days Rob can eat 7*2 kg = 14 kg of potatoes.

which means Jane takes in 6kg of potatoes in 7 days.

Rate of Jane is 6/7

20 kg = amount. SO amount/rate = days

20*(7/6) = 70/3 ~ 23 1/3 (B)
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by truplayer256 » Sat Jun 13, 2009 5:34 am
Rob eats 2 kg of potatoes per day and Jane eats x kg of potatoes per day. We know that when Jane and Rob's rates are combined, they can finish the bag of 20 kg potatoes in 7 days, so:

7(2+x)=20
14+7x=20
x=6/7

So Jane can eat 6/7 kg of potatoes per day, and it'll take her (20)/(6/7) or 70/3 days to eat 20 kg of potatoes. B is the correct answer.
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by bluementor » Sat Jun 13, 2009 8:59 am
x = number days Jane alone takes to finish eating the potatoes.

1/x + 1/10 = 1/7
1/x = (10 - 7)/70
x = 70/3 = 23 1/3

Choose B.

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