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Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in $$1\frac23$$ hours. All three together can eat a whole gallon of ice cream together in 1 hour. How many hours would it take Jenny to eat a whole gallon of ice cream all by herself?

Sep 25, 2018

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Let the portion Jenny can eat in one hour  = 1/x

Let the portion  that  Penny can eat in  one hour = 1/y

Let the portion that Lenny can eat in one hour = 1/z

And we have this system

2/x + 2 / y  = 1      (1)

(5/3)/y + (5/3)/z =  1      (2)

1/x + 1/y + 1/z  = 1   (3)

Multilpy (2)  by  (3/5)  and we have

1/y + 1/z  = 3/5     (4)

Put (4) into (3) and we have

1/x + 3/5  = 1     subtract   3/5 from  both sides

1/x = 2/5  ⇒   x  = 5/2  = 2.5 hrs = time for Jenny to eat the whole gallon by herself

Sep 25, 2018