eating potatoes

[hk]

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

[ssmiles08]

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)

[truplayer256]

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.

[bluementor]

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.

-BM-